competition-math

[torpid cairn]

oh it has an aops page maybe it's important
nvm it's a blog

[rain edge]

same lmao

root flipping

[rain edge]

ye

apparently its like a way of, acc I didnt understand any of the wiki page

[torpid cairn]

"example: this can be applied to problem 6 of IMO.." yeah I will never need this

[rain edge]

lmao

not like im getting into imo anytime soon

lol

i doubt usamo either

[torpid cairn]

my goal is to get into USAMO and then I'll probably get a 0 🔥

[subtle sundial]

goodluck !

[torpid cairn]

thank you 🙂‍↕️

[subtle sundial]

woah

just realized u were talking about usamo

the geometry problems on there are hell

[torpid cairn]

lmaoo that's my worst subject too

honestly I haven't given any of them an honest shot. I probably never will

[subtle sundial]

right. i hate geometry too

whenever i see geometry problems on my olympiads i usually do those last

💔

[torpid cairn]

very reasonable

[subtle sundial]

theyre lowkey fun

once it finally clicks !

but hell to understand

[torpid cairn]

it depends on the problem for sure

I think when it's more than just "here's a bunch of shapes that share some vertices" they can be fun solves! the problem is usually, that's exactly what they are

[subtle sundial]

truth..

[torpid cairn]

I will say geometry when it involves other subjects are some of the most fun and unique problems Imo. i love the combinatorical problems and the ones involving probability (esp. with moving points or something)

[subtle sundial]

right, but when its pure geometry its just tedious

😭

[sweet pewter]

[torpid cairn]

agreed

[rain edge]

ye

its jst torture

[subtle sundial]

i forgot about you guys

sorry

there are some who enjoy this sort of stuff

[rain edge]

💀

Me be wondering why ppl from the past didnt massacre mathematicians cos of the torture tat math gives u

[subtle sundial]

they were probably burned at the stake

[subtle sundial]

[rain edge]

Archimedes lmao, some roman soldier killed him by accident

[rain edge]

hypatia of alexandria

[torpid cairn]

wasn't pythagoras' whole thing getting thrown into the ocean for suggesting sqrt(2) is irrational

[sweet pewter]

no

[subtle sundial]

archimedes had it rough

[torpid cairn]

am I thinking of someone else or did I just hallucinate that

I swear I've heard it somewhere

[rain edge]

????

[torpid cairn]

dawg am I literally making things up rn

😭

[rain edge]

story is that some dude whom he rejected from his school

rebelled against his followers

and they burned his school

so he died

[sweet pewter]

Hippasus

[torpid cairn]

ohhhh I wasn't too far off lmao thank you

[rain edge]

yeah lmao

apparently the pythagorreans were the ones who killed him

evariste galois

younge dude

killed at 20

i think in a duel

[torpid cairn]

that's interesting

[rain edge]

a lot have commiteed suicide tho

maybe math torture

[rain edge]

ye idk

[torpid cairn]

math torture lmao

[rain edge]

im pretty sure galois got involved in some politics stuff

cos i think it was the french revolution time?

idk

[torpid cairn]

yeah that's what the wiki said

crazy actually at 20 solving a 350 year old problem and then becoming a revolutionary

these are the people my parents compare me to

[rain edge]

he got expelled from school too cos he wrote an article abt his school not letting him become a revolutionary

and making him do school work

[rain edge]

lmao

[potent patrol]

hey guys

[torpid cairn]

hii

[torpid cairn]

I think it's good that our current mathematicians don't seem as mentally insane as our old ones

[rain edge]

ye lol

apparently alexandr khazanov another 20ish yr old dissappeared

at 22

yrs

ppl think suicide

acc wait, lets move tis conv to diff channel

tis is comp math channel

[near hill]

Galois died in 1832, several decades after the French revolution -- but French politics was quite unstable and violence-prone for pretty much the entire 1800s, or at least its first half. Galois himself managed to get arrested and jailed (as well as least expelled from his school) for political activism.

[rain edge]

oh i see

but he died in a duel

or so the story is

[near hill]

Yeah, but the circumstances of exactly why (and even whom) he was dueling are rather murky.

[orchid linden]

Unrelated to yalls mathematician discussion lol, but I solved this problem and have a question abt it
my sol - ||assuming all angles are 160 -> then 2080 degrees total, but the sum of all angles in 13-gon should be 1980, so there is an excess of five sets of 20 degrees. Assuming this is compensated by the a 140 and b 120 degree angles, then we have a+2b=5.||
Thing is I kind of just ignore the entire part about the polygon being equilateral, is there a way to know for sure that the problem's unique equilateral polygon is in the set of poylgons I considered(those with angles 160, 140, 120)?

Thanks 🙏

[near hill]

Hmm, we can imagine making the 13-gon by taking a regular 18-gon (with all internal angles 160) and deleting 5 sides -- but the sides we delete, viewed as vectors, should sum up to 0 so the polygon still its together after we delete the sides.

[shadow crag]

Hi

[near hill]

The only way to achieve that seems (much handvawing here!) to be deleting two parallel sides and then three other sides that make an equilateral triangle together.

Having one one of the internal angles be less than 120 would require deleting three or more sides in sequence from the original 18-gon, but that cannot happen if you delete a pair or parallel sides, and three sides that make an equilateral triangle.

[acoustic nova]

I trust this source:

https://mathshistory.st-andrews.ac.uk/Biographies/Galois/

I haven’t heard details about the person he was dueling being uncertain, but I haven’t looked into it so much

[near hill]

I based my remark off Wikipedia saying:

As to his opponent in the duel, Alexandre Dumas names Pescheux d'Herbinville,[15] who was actually one of the nineteen artillery officers whose acquittal was celebrated at the banquet that occasioned Galois's first arrest.[22] However, Dumas is alone in this assertion, and if he were correct it is unclear why d'Herbinville would have been involved. [...] [E]xtant newspaper clippings from only a few days after the duel give a description of his opponent (identified by the initials "L.D.") that appear to more accurately apply to one of Galois's Republican friends, most probably Ernest Duchatelet, who was imprisoned with Galois on the same charges.[23] Given the conflicting information available, the true identity of his killer may well be lost to history.

[near hill]

Instead of the handwaving, one could say something like: If we do delete three consecutive sides from the 18-gon, we have lost a total distance of 1+2cos(20°) in the direction of the middle deleted side. Since 1+2cos(20°) is more than 2, there'd be no way to make up for that by deleting just two more sides anywhere in the 18-gon.

[vernal axle]

I suspect that this was originally checked with a computer. If we ignore the equilateral part then there are only 7 different ordered 13-tuples giving 13-gon whose angles are multiples of 20:
[60, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160]
[80, 140, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160]
[100, 120, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160]
[100, 140, 140, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160]
[120, 120, 140, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160]
[120, 140, 140, 140, 160, 160, 160, 160, 160, 160, 160, 160, 160]
[140, 140, 140, 140, 140, 160, 160, 160, 160, 160, 160, 160, 160]
Further, It's not hard to search through all of the angles permutations to find that the only one equilateral 13-gon is this one (with exactly this ordering):
[120, 160, 160, 160, 160, 140, 140, 160, 160, 140, 160, 160, 160]
That's how it looks:

[orchid linden]

woa cool approach
i think that makes sense to me (?) will needa read it a few more times lol

[orchid linden]

O I see

Tyty yall

[sly pawn]

can someone explain this solution to me?

At the end, when it gets to the 39 part I don't understand

if one set of 2 circles is on the same side (makes sense), shouldn't the other be too?

otherwise if one was opposite sides and one was same side circles, wouldn't one of the smaller or larger circles have to overlap?

Why not just have both on opposite sides and make the answer 78?

doesn't that also work

I thought it should look like this but the ending part confused me

sorry, swap A and B and D and C

because B and D are supposed to be the larger ones

ohhhh

if one pair is on opposite sides then they have different radii comparitively to the pair that is same sided

but why cant both pairs just be same sided like in my drawing?

ohhh

congruent means that they are the same radius, I thought it meant same place and radius

that's why I was confused

I see

[sly pawn]

I was able to solve this one though

this was a good problem

way too slow though

[torpid cairn]

this an AMC 12?

[torpid cairn]

why doesn't the bee just spin in a 12gon here

[reef condor]

It gets bigger and bigger

[reef condor]

Can u do it with arithmetic geometric series and complex numbers faster

[sly pawn]

because the distance increases each time

[sly pawn]

yes you can

[sly pawn]

yeah it was

[torpid cairn]

ohhh I see

[tame elk]

guys how prestigious is the american math olympiad
(as an international student)

[abstract aspen]

Idk but don't do olympiads it's trash

[lyric sand]

How to do olympiads ?

[abstract aspen]

😄

[torpid cairn]

lmao what

is the American math Olympiad different from usamo

[sweet pewter]

true terence tao didnt get 42 points so IMO is trash

[abstract aspen]

Tao himself says that olympiads are not real math

One should more focus on building strong theoritical skills rather than doing "tricks math" , during his highscool

There is plenty of mathematicians who have this view

[valid socket]

https://tenor.com/view/copium-meme-pepe-frog-gif-26117735

[abstract aspen]

Serre said that contests are good for enjoyment but real math is totally different

[abstract aspen]

Do you not share my point

́?

[valid socket]

i don’t

it’s good for developing problem solving skills and to say that it doesn’t teach you math is just dumb

no one’s saying to do elementary number theory when you’re in uni

it’s high school math for a reason

do you think all of high school math is a waste of time?

[abstract aspen]

I mean I don't think it's useless but I feel like a good highscool student have more to gain to dive into abstract stuff than doing what he already can do pretty well.
My point is that knowing that higher math is difficult to have good intuition on, a young mathematician should use his cerebral plasticity for that.

Problems solving skills are good but are not to prioritize over structural comprehension , imo.

Unless you 100% want to be an engineer

[valid socket]

🤔

do you think higher math is just reciting definitions the entire time

[abstract aspen]

Of course not

[valid socket]

i hate to state the obvious but you get better at math by solving problems and in particular, hard problems

there’s no reason to jump on the bandwagon and hate competition math just because it’s a "competition" which is discouraging for people who didn’t get into it or did but didn’t perform as well as they wanted to

[abstract aspen]

And that's my point I think those hard problems a highscooler should do is on analysis or abstract algebra

Or any uni math

[valid socket]

i mean the kids i know who did well in comp math knew loads of analysis and abstract algebra in high school

[abstract aspen]

I think to restrains themselves to basics things, no matter how hard we make them to them

Is not optimal

And barely a waste of time

[valid socket]

some of the ideas are transferable too

[valid socket]

why does this matter

math is supposed to be fun

[abstract aspen]

Is getting better not the primary goal of these guys

[valid socket]

maybe it’s just a passion of theirs

not everyone does comp math for the sole purpose of awards

[abstract aspen]

Sure but people do contests in order to get better at math too and I think if IMO was not considered as the most elitistic thing a lot of them would not even participate and would just do uni math because they would know it is what is optimal

[valid socket]

i think that’s why you’re so bothered by it

[abstract aspen]

Not particularly the awards but there is competition among friends and stuff

[valid socket]

IMO being elitist

like who cares dawg

yea

they’re smarter

so what

[abstract aspen]

Wtf ?

[valid socket]

you don’t think people like luke robitaille are brilliant?

[abstract aspen]

I don't know him that's how I care about IMO so your try to make me look insecure is lowkey patethic lmao

[valid socket]

ironic

[abstract aspen]

Well I don't think I ever looked like I just wanna mess

In this conversation

[valid socket]

you do come off as insecure when you speak like this lmao

like it just isn’t that deep

let people have fun

[abstract aspen]

Well I never said it is that deep I was just having a casual conversation wtf ?

[valid socket]

you’re sat here trying to undermine it as if it’s "fake math" or reduce it to "just tricks"

[abstract aspen]

Yeah and that's just my opinion seems like the one who cares too much about it is you

[valid socket]

i don’t

😭

[abstract aspen]

You're very strange imma just leave the chat bro

Good afternoon

[valid socket]

🤣

[sweet pewter]

[torpid cairn]

ragebait

if not: I'm actually not really sure what your point is, because competition math might be indisputably the best thing a high schooler can do to prepare for higher math. it's fun, social, it draws parallels to problem solving techniques, and it helps you learn theory.

like if your take is "Olympiad don't help you much with higher math" ok maybe you can justify that. probably not. but you opened with "don't do Olympiads" as a blanket statement which is weird

[potent patrol]

lol genuinely

[potent patrol]

critical thinking and problem solving skills are just "tricks" nowadays

[valid socket]

people are just insecure lmao

[sweet pewter]

typical people who said that those problems have 0 applications in life so they're worthless

[acoustic nova]

certainly some level of problem solving is important, competition math to some extent gives that and with harder concepts that are simply skipped over in school

[abstract aspen]

Okay if 4 people told me that then I assume I made a mistake in my formulation, so excuse me for that.
I'm not a native english speaker so my language is probably very little idiomatic.

That said I will clarify my thoughts.
I indeed think that competition math is absolutely not the best way to get better at math, but I didn't say that olympiads don't help you much with higher math. My take is ensencially that one should not prepare himself too much to higher math, but rather do the actual higher math. I feel like your arguments in favor of contests are not exclusive to them, I mean I don't find any added value on olympiads compared to other ways of doing math. Problems solving skills and critical thinking can be developed in hard hitters books (spivak, rudin, lang, hartshorne), as for the social and funny part of it, I don't deny it, but my point is that if you wanna just get better at math, it is far more rewarding to dive into uni math than doing IMO exercises. And I even think that doing both is not optimal.
I'm not close minded and I don't understand why some people call me insecure ? About what ? I don't envy those prodigious kids wtf, I don't even like math I use it as a necessary tool for quantum information, so I definitely don't want to be at their place lmao

[abstract aspen]

Can't we just learn those concepts on a random book, why competition math specifically ?

[acoustic nova]

Well I mean pretty few books teach it. And if u were asking those questions even in a non-competition setting, here is still the appropriate channel

[abstract aspen]

I feel like a decent amount of books teach it, and even if it's not the case I don't really get your point, even if there is only one book that teaches it, why not study it ?

[acoustic nova]

No I mean competition math in general exposes u to problem solving and also interesting math at an approachable level

[abstract aspen]

I would also add to that, that euclidian geometry is purely useless at a higher level, it's principally for a pedagogical purpose, and for the geometrical intuition yes but there is no need to master it to have one.

[abstract aspen]

That's true

For the accessible part of it

I think it is actually a good argument

[acoustic nova]

Why is Euclidean geometry useless

[abstract aspen]

Well it is not a powerful tool for more complex problems

Differencial geometry or complex geometry are more adequate to them

[acoustic nova]

Euclidean geometry is a pretty good tool for hard geometry problems

[abstract aspen]

Since complex geometry is basically a dlc of euclidean geometry I don't see what is the actual value of using it rather than other geometries

[acoustic nova]

there are still several open problems in Euclidean geometry

[abstract aspen]

You're right but the tools used to try to solve them are from other geometries

Mainly algebraic, projective or complex

No researcher use only euclidean geometry concepts in order to solve problems of this field, but rather generalize the problem to more powerful geometries in order to use their tools for solving it

[high goblet]

such as?

i'm sorry euclidean geo is like literally the least useful part of competitive maths

[high goblet]

i mean almost all the euclidean geo problems i can think of off the top of my head are sort-of combinatorial in nature

and you study all of them using other methods, not like angle chasing etc.

euclidean geo (like proving XYZ is congruent to etc.) is pretty much dead as a research field

[acoustic nova]

https://en.m.wikipedia.org/wiki/Category:Unsolved_problems_in_geometry

https://mathoverflow.net/questions/53797/open-problems-in-euclidean-geometry

sure, if you like, it’s more like “combinatorial geometry”

[acoustic nova]

Which parts are better?

[high goblet]

i mean it's still very far from like actual research/uni maths, but at least with something like combi you are thinking about combi

or like with algebra or NT you often have to derive ad hoc bounds for ur arguments, which are useful skills to have

[acoustic nova]

wdym?

[high goblet]

as in like you often come up with like inequalities

or you get a feel for how fast certain functions grow

which can be kinda useful

i mean overall the useful part of competition maths that ur trying to extract for like uni/research will just be the problem solving skills and the resilience to try a problem for a very long time

but yeah as in like the actual content u need for euclidean geo just does not come up at all

[acoustic nova]

Do u have an example? Just wondering

[acoustic nova]

Sure

No wait what about constructions

and like constructibility

[high goblet]

uhh not off the top of my head

but just like in general, knowing that this function grows faster

and like vaguely knowing how you could bound XYZ is a good skill to have

[high goblet]

i mean that's all extremely well understood

also you don't use euclidean geo at all for that, u use galois

ppl got stuck on i.e. squaring the circle or trisecting the angle for too long bcus they were too focused on euclidean geo

when ppl finally brought in galois theory that solved a lot of these problems

[acoustic nova]

I don’t see how that comes up

[acoustic nova]

Ok true

[torpid cairn]

this is reasonable, but still "don't do Olympiads" is not a good way to present yourself

[abstract aspen]

Well that's my way of communicating

Hot take first

Then talk

:p

[proven niche]

ragebaiter:

[warped anvil]

does anyhone have any resources for late aime problems

[warped anvil]

real

[warped anvil]

like late alg geo and nt

i think ill prob just do mont for late nt

and egmo for geo

but what about late algebra?

[torpid cairn]

it's a little disrespectful when you're telling someone directly not to do Olympiads imo

[proven niche]

i dont get the hate on ollympiads

one can still do ollympiads and study higher math later...

[orchid linden]

Oh hey man

[tepid surge]

Toxic and misrepresentative of how math is actually done

Of course if you avoid both of these things then its fine

[proven niche]

yes

you have to have a healthy relationship with ollympiads

[tepid surge]

The problem is that too many people dont

People thinking not getting gold for IMO or smth like that means they arent cut out for math

When in really higher math success is driven by hard work and determination more than it is intelligence

[torpid cairn]

is that really so different from Olympiads though? if I took the AMC half a year ago, my score would be half of what it would be if I took it today

I'm asking this genuinely, because I'm not sure if progress keeps scaling like this

[tepid surge]

Sure but thats for different reasons than practicing higher math does

I suppose you could argue that both comp math and research math need memorization for improvement

But I would argue that comp math is more tunnel visioned in this way

[balmy hound]

any good books for math olympiads

[radiant jasper]

if u are looking for one that has all the concepts(aime- mid usamo level), then u can try pathfinder for olympiad mathematics

[balmy hound]

is challenges and thrill of pre college mathematics good

[radiant jasper]

yeah

if u are aiming for national olympiads, tis won't be enough

btw

you'd need to do several topics based books

like titu andreescu's number theory structures and problems

EGMO by evan chen

u can check out the aops olympiad books recommendation website

[balmy hound]

yea thanks

[valid socket]

so is comp math

people grind all day for years

math is in general

no reason to exclude comp math just because its "toxic"

what makes you think academia isnt toxic

🤔

[tepid surge]

It definitely is

But the kind of toxic that comp math is causes people to have incredibly incorrect perspectives about math readiness or whatever

[valid socket]

i agree that having an imo medal doesnt mean youll have such great success in math and that people shouldnt be so disturbed if they dont have that same success but i also dont think that means we should just try and undermine any form of competition math

[torpid cairn]

I am really curious how strong the correlation is between competition scores and research abilities now lol

I don't suppose there are any papers on this?

[sullen blaze]

they just end up being a quant

[ocean gale]

Assist lads

[ornate blade]

What must the determinant be?

[ocean gale]

Don't have an idea, but that the question

Only that info was given

[ornate blade]

Yes and I'm hinting you

If det A = 0 and det B = 0, what must det AB be?

[ocean gale]

Ohh sorry didnt notice

[ocean gale]

It gonna be zero

[naive sable]

98% highest aggreagate yall!!!!!!!

[ornate blade]

Yep so now just replace B with A and you get det(A^2) = 0

So det(A^2) = 0 and det(A) = 0 implies det(A^3) = 0

Repeat until det(A^2013) = 0

[ocean gale]

Implies det(A^2013) = 0 right?

[ornate blade]

Yep

[ocean gale]

So basically i should just calculate det and equate to zero and solve for x ?

[ornate blade]

Yes!

That's what I wanted you to figure out

[ocean gale]

Shoutout bro, highly appreciate it

Please assist with these

[dusty fable]

Q4 could u let g_1(x)=sin(x), find g_1’(x) then let g_2(x)= g_1(g_1(x)) and find g_2(x) continue this i assume there must be some sort of pattern or cyclical behaviour as sine is periodic

also if no pattern doing it like this will make the brute of it easier as u can just use the derivative of the last term when doing the chain rule

[ornate blade]

Yeah induction is super useful

But you don't need to formally prove it to problem solve

[short rune]

Hello guys, I am a 9th grader in India preparing for IOQM (for those who don’t know it’s the first step of many to get selected to represent India in IMO) does anyone know any good channels to help me prepare from zero?

[abstract aspen]

Disrespectful to who ?

[abstract aspen]

Is this a prank of something

[abstract aspen]

Sure there is probably a correlation but it's because prodigies are pushed by teachers to do contests

If one is a prodigy then he will succeed regardless of if he did comp math or not

[short rune]

Hey @abstract aspen can you help me out if you don’t mind?

[abstract aspen]

So even if comp math is not the best efficient way to do math as a highscooler there will always be that illusion that it is.

[abstract aspen]

I don't know much about olympiads I never really did

[short rune]

Oh, which country are you from?

[abstract aspen]

France

[short rune]

Oh got it

[subtle sundial]

from what i know india has a different curriculum compared to other countries

[abstract aspen]

I just thought of how every undergrad who comes into the discussion share my opinion and how everyone who defend IMO and accuse me of ragebaiting are the highscholers who do IMO...
I feel like some people should be more open minded

[subtle sundial]

i doubt anyone here is an imo medalist

[subtle sundial]

https://artofproblemsolving.com/community/c3176_india_contests

[abstract aspen]

Yeah IMO I mean comp math

[subtle sundial]

mmm i’d say competitions have their fair share of pros and cons

though based on my experience theyve helped alot

you do have a point

[short rune]

I don’t know about other countries syllabus but the most important topics I can tell you are algebra, geometry, number theory for ioqm

[subtle sundial]

i see, it shouldnt be too hard honestly to brush up on those

[short rune]

So if you know some good materials or yt channels pls do share

[subtle sundial]

here u go man

hmm for number theory i'd probably go watch prime newtons

[short rune]

Ig there are only PYQs in it but I need someone to explain concept pretty well

[short rune]

Ok…

[subtle sundial]

also michael penn, if you're able to understand notations

[short rune]

Which notations like example?

You mean sigma notes?

[subtle sundial]

the basic stuff

yep yep

[short rune]

Sigma and Pi notes is a concept I am exploring rn

[subtle sundial]

nice !

[short rune]

I have a book if you wanna know the topics you can check it’s index

[subtle sundial]

sure, if you'd like* to share

[short rune]

It is Pathfinder by Prashant Jain for Ioqm

[subtle sundial]

i see

whats a prmo?

[short rune]

Like ioqm was previously called pre-Rmo

Rmo is just the next stage after ioqm

[subtle sundial]

sounds fun man, good luck !

[short rune]

I really don’t know how I will perform since the exam is in less than 2 months atp

[subtle sundial]

hmm i see

[short rune]

And I really don’t understand the creativity to solve those problems

[subtle sundial]

that is tough

[short rune]

Yk just randomly multiplying with a random variable in the middle of the solution to get the answer

[subtle sundial]

hmm

[vale geyser]

Guys I am searching for someone to do group study on regular bases.
Topic - Differentiation.
Anyone down? Plz DM me..

[subtle sundial]

its usually pattern recognition

inuition if you will

[short rune]

Yea, do you know how to improve it?

[subtle sundial]

what i do is solve olympiad questions from my countries papers

even if i am not able to solve them, i take a look at the solution

[short rune]

Hmm…

[subtle sundial]

try to understand the reasoning behind the steps others have done

[short rune]

I am not able to solve many of the questions

That makes me lose confidence

[subtle sundial]

dont worry man, confidence builds over time

[short rune]

Yeah… thanks for the help man appreciate it, gtg

Bye

[subtle sundial]

no worries, goodluck mate

[short rune]

Thanks mate, bye

[sly pawn]

does anyone know the formula for arithmetico geometric series like s(n) = a^n * (b+dn)?

[near hill]

You roll into a channel dedicated to a particular hobby and aggressively tell the people in it that their hobby is useless and they should be doing something else instead.
It beggars belief that you cannot see how that is ragebait.
You could be saying analogous thing in a channel for tennis players or stamp collectors (hmm, do stamps even still exist in 2025?) and get a similar reaction.

[sly pawn]

you don't like olympiad math?

[abstract aspen]

It's probably one of the things in math I like the most doing it

[sly pawn]

you don't like math competitions then?

[abstract aspen]

No I'm just saying that it is not suitable for optimal training and some psycho-rigid guys make me a lawsuit

[sly pawn]

okay

but it is very good to learn problem solving

[near hill]

Why does a hobby people have fun with need to be "suitable for optimal training"?

You seem to have a really bizarre set of requirements for which kind of fun you can abide people having.

[sly pawn]

idk, there will always be people looking for "optimal" method but usually the people who just go through things with a good procedure overall get more done

[abstract aspen]

I think most of people would not do it that much if they would know that it rather hinders the progression

[abstract aspen]

Are you trolling ?

[near hill]

You think most people would choose not to have fun with the thing they have fun with, just because you hate on it?

[sly pawn]

how does it hinder anything

you get worse at math from doing competition math?

[abstract aspen]

That's what I said you're psycho-rigid, you're not even trying to understand me

[near hill]

Apparently spending any time on an activity Tenzr doesn't approve of "hinders" someone's time to do things Tenzr does approve of.

[sly pawn]

wait this explains a lot

[abstract aspen]

hahaha

[sly pawn]

lolol

[near hill]

Why should people even care about whether you have something against the activity they choose to spend their free time on?

[abstract aspen]

No but it will make your progress slower than if you just directly dived into higher math

[abstract aspen]

You're making me say things I didn't ever say

[near hill]

So you have something against people doing anything that is not rigidly forcused on "progress" towards a goal that you approve of.

[sly pawn]

well yeah because you aren't studying higher math for competition math

[near hill]

You're the one who rolls into this channel and try to tell people they shoudn't be having the hobby the channel is about.

[abstract aspen]

I'm genuinely interested to discuss about that to find what is true and I'm not close-minded.
On the other hand you just want to make people look like evil while nobody cares or at least should care

I swear you are the one who is agressive on the language

[sly pawn]

studying for competition math is more studying for problem solving abilities and maybe getting really good at like combinatorics and number theory for the higher math part

[sly pawn]

ye fr

you right about that one

[near hill]

And you are the one who is aggressive on substance when you swoop into a channel dedicated to a particular hobby and tell people they shouldn't be having that hobby.

[sly pawn]

but I think your premise is flawed

[near hill]

Telling people you disapprove of them having fun tends to make them push back. Whoda thought?

[sly pawn]

no

[near hill]

What?

[abstract aspen]

I agree but I think some other ways are better for this purpose.
I made a more developed message a bit ago I will find the link

[sly pawn]

He is assuming that people do competition math to progress towards higher math, this is not the case. People participate in competition math probably more for the competition, problem solving, and general math ability.

[sly pawn]

Okay

[abstract aspen]

#competition-math message

[near hill]

All of that is still a really rotten excuse for telling people they shoudn't be having fun with the stuff that's fun for them.

[sly pawn]

That might be so, even for the skills like problem solving, but I don't believe there are any competition-based programs that help work on these abilities too as well developed as competition math is.

[sly pawn]

He never said that but ok

strawman or smth

[near hill]

That's his entire point!

[abstract aspen]

Then it is probably a cultural thing in France and you were right about that, but out there everybody does it for the sake of competition

[sly pawn]

Yeah definitely a strawman of his point

[sly pawn]

I see, that makes more sense from your perspective then

[near hill]

don't do olympiads it's trash

[sly pawn]

Bad opening, he further explains his point later

I agree, that is a bad way to start though

[near hill]

"Don't do olympiads it's trash" was literally the guy's very first post in a channel dedicated to likers of competition math.

[abstract aspen]

I mean I aleready explained the motivation of this one.
But I just don't understand all the hate, even if I was indeed a piece of shit then who cares just ignore me I really don't get it.

[near hill]

All of the subsequent posts have not presented a single good reason why you think people shoud "don't do olympiads" and the thing they choose to have fun with "is trash".

[sly pawn]

Because when you attack something people like, most people automatically feel offended personally and feel they need to defend it

[near hill]

Calling people's chosen way of fun "trash" is inherently a way to pick a fight withe them.

[abstract aspen]

Then you misunderstood me because I think I was as clear as I could

[sly pawn]

90% of people are close minded and won't listen to you if you are immediately on the attack

[near hill]

There are not a lot of ways to understand "don't do olympiads it's trash".

[sly pawn]

Yes there are, for example:

"Why do you think that?"

[near hill]

And the explanation we got at lengths is that apperantly Tenzr considers any activity "trash" if it is not strictly focused on becoming better at higher math, or something.

[abstract aspen]

That's anyways not what I wanted when I said that so all of your accusations fall appart

[abstract aspen]

Yeah I see

[near hill]

What did you want when you rolled into a channel to call people's hobby "trash"?

Does "trash" somehow have a meaning in your language that is not an attack?

[sly pawn]

That is not correct. From his cultural perspective (I assume), competitive math's focus in France is mostly on reaching towards high level math. Now, this is not the case in most of the world I believe, and that's why there is a disconnect between your two perspectives. He sees it this way, rather you see it as just a hobby that you like to do and have fun with. That's why a point he thought was pretty reasonable makes you so angry.

[sly pawn]

He's French

[near hill]

Does "trash" mean something positive in French?

[sly pawn]

😂

[near hill]

Does "trash" even mean something it's remotely okay to like in French?

[abstract aspen]

I would definitely change the tone next time since people seems to not have the same philosophy of debate as me.
As I said it is my way of communicating, I'm more dialectical than diplomate so I usually don't really care about the form.
But even if they are way too psycho-rigid it's not my intention to hurt anybody so I guess I would make some efforts.

[near hill]

Calling people who disagree with you "psycho-rigid" does not really win you any points either.

Doing it in the same sentence as "it's not my intention to hurt anybody" evidences a certain chutzpah, though.

[abstract aspen]

No I don't call people who disagree with me psycho-rigid I only call like that people who take it personally

Like you

There was some people who didn't btw

[near hill]

I'm not taking it personally, but I'm totally flabbergasted at how you don't see it enrages people when you call something they like "Trash".

[abstract aspen]

And that's why you're psycho-rigid, being flabbergasted by this sound crazy to me, I'm a random guy on a random channel of a random discord server, take it easy man

[near hill]

Again with the insults.

[abstract aspen]

Are you joking or something

[near hill]

Why would I be joking?

[abstract aspen]

I didn't insult anybody the other guy is right about strawman

[near hill]

You've at least two time written "you're psycho-rigid"

[abstract aspen]

I'm wasting my time good afternoon

[near hill]

And then you propose it's a joke to call out those insults?

[proven niche]

holy shit this guy

if you dont like ollympiads dont do them

dont come to the ollympiad channel

and constantly talk shit about them

you're so annoying

like we get it

you're not making us stop doing ollympiads

[prisma python]

well maybe because this channel is for competition math and he just said competitions are trash

i wouldn't assume anyone would be happy if i said that chess is trash in the chess channel

[abstract aspen]

And y'all crying about that, crazy

Imma mute this chan

[proven niche]

please do

[abstract aspen]

I would ask you to not ping me if you want me to do not talk here

[proven niche]

https://tenor.com/view/guy-arguing-guy-talking-to-wall-talking-brick-wall-gif-18667615

[abstract aspen]

So who's ragebaiting now

[torpid cairn]

ngl you showed up to "#competition-math" saying "don't do competition math" did you expect us to agree with you 😭

[proven niche]

fr

[abstract aspen]

Just for those reactions I take back my apologies

Hope you like my new nickname

[wanton ridge]

<@&268886789983436800> pretty sure this is not the most appropriate nickname; they're trying to ragebait

[somber belfry]

Please keep channel on topic, thanks

[sacred perch]

can someone explain how the answer isn't 67

i basically did 2(2x+z) + 3y = 2009
so 2(g) + 3y = 2009 (g = 2x + z)
and uh now one solution is g = 1003, y = 1
now the standard step i subtracted the coefficients of y from 1003 and added coefficient of g to 1 until g>=1
which gave me 334 sols
same with the other equation which gave me 333 sols and adding both we get 667 = 67 mod 100

the answer is apparently 68 but i would appreciate if anyone can answer where i went wrong

[ocean gale]

18 and 20 are very easy for me, can anyone assist with the rest🙏🏼🙏🏼

[near hill]

Sounds like you're only counting one solution for each value of g?

[sacred perch]

yeah

i couldnt figure out another way

i porbably undercounted

[near hill]

g=1003, y=1 alone is 501 different solutions for x and z.

[sacred perch]

i see any idea how to approach as to count all solutions?

would i multiply 501 * 334

to get number of solutions for g

[near hill]

No because g=4, y=667 is only one solution, namely x=1, z=2.

Not immediately sure what a smart way to count would be.

[sacred perch]

it seems like the number of total solutions is a very large number from chatgpt

[near hill]

I wouldn’t trust GPT for either reasoning nor arithmetic here, but eighty-odd thousand sounds like the right ballpark.

(Namely about half of 501×334)

[sacred perch]

hmm yeah ill think about it

thanks for your help

[ebon copper]

15.) sin(3x)/sinx = [sin(2x)cosx + cos(2x)sinx]/sinx
= [2sinxcos^2(x)]/sinx + cos(2x)
= 2cos^2(x) + cos^2(x) - sin^2(x)
= 4cos^2(x) - 1

given: cos(3x)/cosx = 1/3
[cos(2x)cosx - sin(2x)sinx]/cosx = 1/3
cos(2x) - [2sin^2(x)cosx]/cosx = 1/3
cos^2(x) - sin^2(x) - 2sin^2(x) = 1/3
4cos^2(x) - 3 = 1/3
4cos^2(x) = 10/3

sub into previous expression;
sin(3x)/sinx = 4cos^2(x) - 1 = 7/3

[ebon copper]

19.) defining s_n := x_n/(1 + x_1 + ... + x_n);
(x_n/s_n) + x_{n+1} = (x_{n+1}/s_{n+1})
(x_n/x_{n+1})/s_n + 1 = 1/s_{n+1}
s_{n+1} = x_{n+1}*s_n/(x_{n+1}*s_n + x_n)
we note x_n > 0 so s_{n+1} < s_n; therefore s_1 is the largest number in the sequence s_n
hence we maximise
x/(x+1), 0 <= x <= 1
= 1 - 1/(x+1)
maximum occurs when 1/(x+1) is smallest, at x = 1
1/(1+1) = 1/2
z = 1/2

[radiant jasper]

hello,just curious but what exactly was your percentile?

[ocean gale]

Thank you so much, highly appreciate it

[runic pasture]

16. Let X,Y~U(0,1) and suppose (wlog) max(X,Y)=X=c. Then, Y<X necessarily occurs with probability F_Y(c)=c. There are 2!=2 ways to arrange the max (either X or Y), so the density function of the maximum will be f(c)=2*F_X(c)*f_x(c) (note that F_Y = F_X as they both follow the same distribution), so E[max]=integral(c=0 to 1 of c*2*c*1 =2c^2)=2/3.

General remark, the density function for the maximum of n observations from one continuous random variable, X, is always n*(F_X(x)^(n-1))*f_X(x) and can be easily shown by induction on the argument above

[warped anvil]

yo hello

[near hill]

Don't crosspost between several different channels. It's wasteful because people risk using time on typing answers that have already been posted elsewhere.

[torpid cairn]

probably not a whole lot

if you took AMC today what do you think you'd get?

[true grotto]

a solid 30

it’s in 4 months

any tips to prepare

all I want is AIME qualification

[torpid cairn]

for AMC 10/12? I'd say that's probably the bulk of it

i was in the same boat about 6 months ago (maybe ~10 higher) and now I think I'd get a 110-120. I would start by going through the tests on aops and solving them under time pressure.

you probably shouldn't need to learn many theorems but if you look at a solution on aops and it uses a strategy you don't understand I would try to click thru any of the hyperlinks to see what you're missing

tldr just do practice tests

cc @true grotto

actually 10 correct was probably higher than what I wouldve gotten so u got this

[true grotto]

not aops books?

do you have any idea of by which grade the average student qualifies for AIME?

if they do

[torpid cairn]

not sure how much they help but they're definitely not required

still, you should probably ask someone who's actually read them

[torpid cairn]

I was wondering this too actually

I don't think there's data on it. pretty much all we have is the score distribution and none of it is aggregated by grade

yeah that's completely fair

you definitely will learn as you just do the problems. they're quite similar, generally

[rain edge]

maybe comp math books

not the normal ones

[torpid cairn]

js read solutions when you get something wrong

for 12? I believe so, yes

[rain edge]

lmao I have the book in front of me rn

[torpid cairn]

for 10 it's alg 2

going into precalc next year but I know ~all of the content I need for AIME

generally you should know the trig functions, logarithms and some basic properties, and product/sum notation ( represented by sigma and capital pi)

you too 🙂

[true grotto]

I’ll just try them once by buying maybe one

[true grotto]

that’s true, kind of unfortunate, if they did I would have an idea of the competition there is

[true grotto]

oh shii, which one?

do you guys think a person could finish all aops intro books in 4 months…

[rain edge]

alg intro, but i alr know evrything in it, so im jst doing it for fun

[rain edge]

YES!!

[true grotto]

no way…

[rain edge]

im done with a little more than half of the first one and i started like june 20ish

intro to alg

its the bigst one

[true grotto]

nah the intermediate algebra one is

[rain edge]

but tats not the intrio books

[true grotto]

that’s like 25 days ago, but I have 4 months until AMC10

[true grotto]

yea true

[rain edge]

yes grind

ill do it with u

im tryna finish bfore school starts

[true grotto]

bet

that’s motivating

add me

gtg I’ll cya later

[torpid cairn]

I'm curious would u say the book has helped you?

[rain edge]

nope

atleast not the intro books

but if u want like acc comp stuff then do the aops comop math series

ive finished the last one, rlly helpful

[torpid cairn]

yeah I've heard they're like AMC 8 level, would u agree with that

[rain edge]

ye

i took amc8 last yr

im going 9th rn

[torpid cairn]

what'd u get

[rain edge]

22

i missed a counting thingy

[torpid cairn]

higher than I ever got lmfao

[rain edge]

5th q

[rain edge]

i was one point away from DHR 😭

[torpid cairn]

dhr was that high??

[rain edge]

lol

[rain edge]

23

[torpid cairn]

crazy

I think I got 17

ngl I kinda sucked

[rain edge]

but i guessed last question and got it right smhow

[torpid cairn]

right

[rain edge]

i mean 17 aint tat bad

[torpid cairn]

yeah but I mean I would probably be doing a lot better rn if I started taking comp math seriously in middle school

[rain edge]

ye, i wish i had started off more seriously in like 6th and 7th grade

r u gonna take amc 10 or 12??

next yr

[torpid cairn]

10

incoming sophomore

[rain edge]

i see

idk how im gonna take it tho, cos my hs stopped offering amc

[pallid tundra]

do they still offer it online?

if so you might want to ask around and find a school offering it

[proven niche]

if you have a lot of time yes

maybe 2 hours p/day everyday

[proven niche]

dont do just theory for amc10

you should focus on doing lots of problems

and if you realize you're getting questions of the same theory wrong a lot

then learn that theory

you need to do WAY more problems than you need to learn theory

learned this the hard way after wasting half a year and honestly learning nothing for actual problems

well, that is if amc10 is similar to the brazilian math ollympiad

yeah nevermind amc10 is multiple choice

but still, solving problems is number 1 priority

[torpid cairn]

idts

[torpid cairn]

mine doesn't either, check local colleges

I emailed MAA asking for locations and they gave me a list of local ones. there's also a website that shows local spots but it's been down (they said it'll be back up in some weeks)

[pallid tundra]

ah was it just a covid thing then

I remember doing it online my junior and senior years (feb 2021 and nov 2021)

[rain edge]

oh I see!!

[rain edge]

im prob gonna ask one of the other hs in my area who do offer it, or go to a private org

like aops or think acadermy or smth

[torpid cairn]

we were supposed to but the proctor wasn't able to get it running so we just did it on paper loll

[orchid linden]

if amc was online then cheating 📈

[ornate blade]

There's already massive cheating in for example, Mainland China so...

Paper does disincentivise cheating

But if students are so fixated on cheating out of desperation (a lot of Asian unis give preferential admission to Olympiad winners) then it's hard

[untold thunder]

Can someone draw a quick diagram or explain this because I'm unsure how this is possible

[sweet pewter]

?

[untold thunder]

nevermind I just figured it out

I didn't know the points could go outside

[orchid linden]

lmbo

realization

[lofty atlas]

thoughts?

[urban parcel]

man im tryna do amc 12 as a freshman next year

its not even real math bro

[true grotto]

yea problem solving helps a lot

To reinforce concepts

[soft vigil]

for sure

and if there are small gaps in knowledge

they get filled through lots of problems

[runic pasture]

no clue how helpful this is, but it may be worth trying to write a_n explicitly (which seems very doable) and then some kind of induction argument from there on a_(2n)*b_(n+3). It is likely helpful to note that the numerator of the b_(n+2) recursive step can be factored via sum of cubes

[torpid cairn]

can u even do 12 as a freshman

I mean regardless you should do 10

[runic pasture]

yes, you can always test up for amc

ik i did

[torpid cairn]

I assume it's not really worth your time?

[runic pasture]

its good practice ig

[torpid cairn]

unless you wanna do usamo instead of jmo ig

[torpid cairn]

but you can't do both 10 and 12 right?

[runic pasture]

u can do 10a and 12b or vice versa

but not 10a and 12a

[torpid cairn]

hmm okay I was unaware

[runic pasture]

as they are tested at the same time

[torpid cairn]

and you get fully registered for both so you can qualify further?

that's cool if so

[runic pasture]

yep! so if the cutoffs for aime are more friendly for the 12a instead of the 10b, you can qualify thru the 12a

[torpid cairn]

cool!! that actually helps a lot lol AIME should be a lock if I do that

thank you 🙂‍↕️

[runic pasture]

yeah np!

and good luck!

[pallid ginkgo]

this reeks of some fibbonanci stuff, just try to shove fibbonanci into it and pray it works

[prisma python]

yeah a_n is just k^(nth fibonnaci number) i think

[lofty atlas]

Yes. I could not solve k=1 case without a_n anyway.

[near hill]

But the $b_n$ are weird. If we write $c_n=k^{F_{2n}}b_{n+3}$ (which is what we're supposed to prove is an integer) and translate the recurrence for $b_n$, I get
$$c_n = (k^{F_{2n}-3F_{2n-2}+F_{2n-4}}) \frac{c_{n-1}^3 + k^{3F_{2n-2}}}{c_{n-2}}$$
where the initial factor of $k^{F_{2n}-3F_{2n-2}+F_{2n-4}}$ is always $1$ and drops away.

[gilded halo]

Troposphere

[lofty atlas]

Interesting. Looks like the right move. It still reduces to b_n in the k=1 case. I suspect that case is not too difficult but my number theory is poor so I could not do it.

[near hill]

If we're lucky, each c is just an integer polynomial in k. The degree of c_n would end up being 3F(2n+2), meaning that the k^3F(2n-2) gets added in the middle of the terms of c_{n-1}^3 ... which doesn't really seem to bode well for this approach.

[near hill]

Actually, since only a_2n matters, the important thing here is probably really the recurrence for even Fibonacci numbers: d(n) = 3d(n-1) - d(n-2), and d(0)=0, d(1)=1.
Starting with hand-computed facts

c_0 = k³+1
c_1 = (k³+1)³+1 = k^9 + 3k^6 + 3k^3 + 2
we then have, assuming it is true that c_n is always an integer polynomial in k:

• the degree of c_n is 3d(n+1)
• the leading coefficient of c_n is always 1
• the constant term of c_n is 2^d(n)
  (still not sure if this leads anywhere, though)

[warped anvil]

Does anyone have any resources for late aime problems

Like the number theory theory for late aime

[rare bluff]

I mean is this intricate equation right anyway??

seems heavy to me

[sweet pewter]

bruh I know where you get this from

[rare bluff]

what youre talking about anyway

I don't truly understand

[rare bluff]

yea you must think about using the google lens to find its origin

[subtle sundial]

aye smth like that ✌️

[near hill]

What does \sum_{eye} mean, anyway?

[sweet pewter]

cyc

cyclic sum

[near hill]

Ah.

[torpid cairn]

what is this 😭

[orchid linden]

zawg

nah they forgot a negative sign

[dusty fable]

can someone help me with question where it is like minimise something given that the variables satisfy some other equation

eg

But this one idk

This ones easy I did it with trig y=Rsin(m), x=Rcos(m)

[ivory ember]

,w factor x^3+y^3+z^3-3xyz

[gilded halo]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by civil_service_pigeon

[ivory ember]

Use that ^

[rain edge]

wth

[orchid linden]

Umm maybe look into AM GM HM inequality

Cauchy schwarz

and also try random algebra manipulation stuff if needed to get it to work

[orchid linden]

yeah you prob need AM-GM for this

[dusty fable]

i know AM gm where AM> GM but how does that help can u like run through the problem for me

[radiant jasper]

👁️

[dusty fable]

oh that’s interesting

[ivory ember]

Yeah and then it’s typical AM GM like you said

Big hint: ||u=x+y+z, v=x^2+y^2+z^2||

[minor yarrow]

hello

do you guys know if they release the scores for mathcounts if u didnt make states

[vernal axle]

These questions keep going in circles #competition-math message

[ivory ember]

#bruhmoment

[dusty fable]

lol

[radiant jasper]

Hey guys!

[subtle sundial]

welcome

[topaz arch]

Heyy, I'm in grade 10, and my math teacher signed me up for a math contest against our province, and I was wondering what do y'all think I should review ?

[subtle sundial]

mm depends on where you're from

if you can i'd look for past papers on that contest

but if you can't i'd focus on number theory

also brush up on geometry theorems + combinatorics

[pallid dragon]

nothing, who cares

like it sounds this is your first time, just see how you do with no preparation

i went to state comp with no preparation, not in math though

[prisma python]

it's still good to study
i think if you want to see how well you do just use a past paper and time yourself

[rare bluff]

combination and Newton's binominal sum seems quite easy but geometry seems little hard

anyway

I need an expert to explain about this intricate integeal

[orchid linden]

brother

get out of comp math 😭 go to #1021175428326633542

[orchid linden]

ya just mock past tests prob

[orchid linden]

hola

[foggy python]

aw hell nawww

[rare bluff]

<@&268886789983436800> random things???

[versed dagger]

This doesn't look like competition math

[golden cradle]

consider #calculus

[foggy python]

this sh* scared me

[versed dagger]

you should follow @orchid linden 's advice and go to a help forum

[rare bluff]

okay

[orchid linden]

wait whered you go to get access to this channel

dont see it in the roles

cause im wondering if theres linear algebra lol

[pallid tundra]

p sure you just need the undergrad role

[sweet pewter]

use power of point S to prove ∆SAP and ∆SPB are similar

then it's just angle-chasing to prove angle KCM = LCM

[candid prairie]

you dont actually need the role btw

can just add the channel

[pallid tundra]

oh icic

good to know

[torpid cairn]

are you smurfing in the math discord

no one here is gonna help you bro 😭🙏

[foggy python]

people do help actually

[torpid cairn]

with a calculus problem in the channel for competitions which pretty much never require calculus?

[orchid linden]

nah i think they genuinely want to know cause they sent it into the multi var channel afterward lmbo

or maybe just smurfing idk

[rare bluff]

keep maintaining on main topic pls

I'm asking in wrong channel and don't wanna break the topic you guys know, it's quite embarassing for me.

[torpid cairn]

my bad bro

[orchid linden]

👍

[sleek ravine]

<@&268886789983436800>

almost pinged a guy called yamal, not sure how

[zinc tundra]

guys

how bad is AMC 10 and 12

whats that rigor looking like

[torpid cairn]

I dont think it gets much easier

in terms of comp math

[zinc tundra]

like wdym

i heard amc 10 is pretty easy if your ahead of the curve

oh nvm i was reading it wrong

[orchid linden]

relative to what

just take a mock tbh

[zinc tundra]

yeah i did its lowkey light

[wanton ridge]

<@&268886789983436800> here too

[warm rock]

how long did it guys take you to go from scoring low on amc 10 to qualifiying for AIME?

(assuming you haven't been doing comp math for a while)

[coarse shuttle]

Need a lil advice:

I mainly do aime problems

Sometimes I like to try olymouf problems

But sometimes, even after looking at the solution, all I can do is say WTF

Idk why phone make its all caps

But like, I won’t be able to think of a single step in the solution

[cosmic mesa]

U gotta learn concepts first and (very importantly) understand why they work the way they do

Conceptualizing problems is probably the most important thing here

[coarse shuttle]

i know the stuff ig

but its just like

the manipulation

this is an example fro mtdy: N7 (RUS) Let P(x) = anxn + an−1xn−1 + · · · + a0, where a0, . . . , an are integers,
an > 0, n ≥ 2. Prove that there exists a positive integer m such that P(m!) is a
composite number

my friend asked me this problem from imo shortlist

and the only tool i could think of was using b-a | P(b) - P(a), and I was trying to get some contradiction by assume all P(m!) were prime

but the solution involved a lot of what felt like random manipulation

[orchid linden]

O dam go you 👍

[zinc tundra]

what math are you taking right now

[warm rock]

i finished alg 1 and geo in school math

im reading aops intro books rn

before starting comp math i took an amc 10 and got 49,5

[zinc tundra]

dang

amc 10 has alot of alg 2

[zinc tundra]

once you take alg 2 at least for my school you get a lot of insight on number theory and a lot of sub topics ig if you can put it that way

im assuming ur like

9th or 10th grade

[warm rock]

rising freshman

[zinc tundra]

prolly try to qual aime before u do amc 12

[warm rock]

yep

do u think i have a chance this year?

[zinc tundra]

u finished geo?

and alg 1?

[warm rock]

mhm

[zinc tundra]

at least geo is still fresh in ur brain

but uh

u might need to self study alot of alg 2 topics

like all the functions

radical, rational , quadratic, polynomial yk stuff like that

but one thing is

[warm rock]

im just curious bc idk - how does that help (genuinely asking)

[zinc tundra]

wdym

[warm rock]

im not very experienced but i heard comp math is very diff from school math

[zinc tundra]

amc 10?

[warm rock]

and also wouldnt i need a calculator for a lot of that stuff

yeah

[zinc tundra]

its not that different

[orchid linden]

I’m prett sure 0s school is just good

lmbo

[zinc tundra]

you could compare it to SAT or PSAT math probs

imo

[orchid linden]

my school did not give me anything to work with for comp math

[zinc tundra]

💔

we got sat prep with our alg 2 course

a little amc

[warm rock]

i was thinkin ab studying alg 2 anyways so i could skip precalc

my school has never had an aime qual

[orchid linden]

O lmbo

[zinc tundra]

bro what

[orchid linden]

broo what

[zinc tundra]

IM SERIOUS

[orchid linden]

Wel I can see it a little

[warm rock]

so if i study hard and learn a lil alg 2 yall think its possible?

[zinc tundra]

yeah practice practice

[warm rock]

dont lie btw

[zinc tundra]

anyone can do it with enough practice

dont fact check me on this

[orchid linden]

Like the last maybe 3 questions on the sat math portion are comparable to like question 7 on the amc10

[zinc tundra]

module 2

is similar

ish

ish

[orchid linden]

yeah module two like last problem or so

[zinc tundra]

the more i think about it

the worse it gets

hmmm

[orchid linden]

lol

[zinc tundra]

i should reconsider

[orchid linden]

Well like

[warm rock]

trust i will qual 'jmo 10th a

[orchid linden]

practice a ton

[zinc tundra]

fr

[zinc tundra]

me personally i do usabo

[warm rock]

nice

im tryna become a quant

so usaco and usamo rn

[zinc tundra]

dang

good luck

usaco is mad hard

[warm rock]

i need that luck

ngl

[zinc tundra]

why are u tryna skip pre calc

[orchid linden]

😔 i need that luck too

[zinc tundra]

yygs calling my name

[warm rock]

all the prestigious math summer programs (PROMYS, and a few others) have ppl finishing high school math in 10th

i wanna get in

so hopefully i take calc bc in 10th

[zinc tundra]

brother what is this comp

SUMAC only accepts MO/IMO medalist

[warm rock]

yeah sumacs out of the question for me

[zinc tundra]

someone i met doing some harvard class got into sumac by "listing some medals"

lowkey just erase me now

[warm rock]

im trying so hard not to compare myself to others

[zinc tundra]

lowkey same

ur one year younger than me

insane work

i was not try harding freshman year

[warm rock]

i realize i be putting my selfworth on my accomplishments - but there will always be someone better

so atp im just in a trap

[zinc tundra]

🔥

[orchid linden]

well if it helps im a rising junior and have yet to qualify aime

[zinc tundra]

💔

lock in twan

[orchid linden]

🥀 94.5

[zinc tundra]

WE all qualifying AIME this november

[orchid linden]

fr

[warm rock]

yes

my only worry is my career

[zinc tundra]

we are scoring 130

[warm rock]

bc ive always wanted to do cs but that got oversaturated

then ai but also got oversaturated

and now quant which is cooked also 😭

i only care ab college bc im scared i wont get a job

[zinc tundra]

are you doing summer programs?

also did u do amc 8

[warm rock]

nope

completely new to comp math

i wanna do awesome math next year

[zinc tundra]

idk how many international math comps there are

i only know bio

[warm rock]

me neither

[zinc tundra]

dang u should def start learning alg 2 and beyond

someone check me on this

isnt there precalc on amc 10

[warm rock]

there is but prob not necessary

[orchid linden]

nah technically idt so

i think amc10 is only supposed to include up to 10th grade math

but knowing above helps a lot

[warm rock]

i heard that with enough higher education (calc+) u can brute force half problems

[orchid linden]

hm

[warm rock]

like area questions

[orchid linden]

i did take calc bc

O

yeah

sometimes its applicable to optimization problems

[warm rock]

👍🏽

what classes did u skip

to take bc in 10th

[orchid linden]

i learned everything through aops so freshman year I just jumped from math 2 -> calc ab

[zinc tundra]

bro omg i js saw 2024 AMC mock

i might be cooked too

[orchid linden]

in my school you needa take AB before BC

[zinc tundra]

💔

[warm rock]

what is math 2?

[orchid linden]

oh

[sleek ravine]

ur school sucks

[orchid linden]

its basically like geometry combined with algebra or smth

idk integrated math 2

[warm rock]

idk

[orchid linden]

i skipped it so idc

[orchid linden]

fr

[warm rock]

private or public

[orchid linden]

no higher math offered after BC so i needa go to community college

public

[warm rock]

me too

[zinc tundra]

linear alegbra 💔

[orchid linden]

lol

[zinc tundra]

future dynamic geo students

have fun!

[warm rock]

trust

i will phd in math

i might acc if quant fails

[sleek ravine]

i thought you wanted a job

[warm rock]

^

every single job (yes, every one) thats STEM related is at risk of AI

i might as well choose the job tha pays the most and interests me before ai fires me

[sleek ravine]

CS majors getting cooked

[sleek ravine]

fr

[warm rock]

i used to wanna go into cs

realistically

worst case scenario i js get phd in math and then become an actuary

[sleek ravine]

how is that the worst scenario

[warm rock]

ur right

worst case is im unemployed

[sleek ravine]

if thats the worst scenario then u got nothin to worry about bro

yeah exactly

[warm rock]

but idgaf ab insurance

so i dont rlly wanna be an actuary

[zinc tundra]

yo mark cuban told me actually the job market is not cooked

[sleek ravine]

insurance is for unlucky people

(i am an unlucky people)

[torpid cairn]

I feel like quant has to be cooked

[warm rock]

😭

[torpid cairn]

moreso than everything else

[warm rock]

more than cs?

[torpid cairn]

I mean math specifically

[sleek ravine]

the only thing more cooked than cs is art history major or gender studies major

[torpid cairn]

not software engineering jobs

[warm rock]

at LEAST quant isnt oversaturated. sure its hard asf to get into but they still need ppl. unlike cs, where theres too many applicants

[zinc tundra]

bro, he said that everyone is overreacting abt AI and that many STEM jobs ( literally only doctors) won't be fried

[torpid cairn]

right

I don't like mark cuban

[zinc tundra]

anyone here doing HVTSp

[warm rock]

if u look up "mechanical engineering job market" youll find a reddit post saying it sucks

iirc

[orchid linden]

id air on the side of taking the part about "overreacting" with a grain of salt

[sleek ravine]

if you look up jobs for physics or math majors, some of the top results are usually engineering jobs

._.

[warm rock]

no job in stem is good unless ur smart and talented

atp

[zinc tundra]

💔

[orchid linden]

cause AI progress is probably a lot faster than a lot of people think

[torpid cairn]

if there existed a button in front of you that would destroy genAI forever would you guys press it

[zinc tundra]

engineering is the safest major ( am i cooking)

[warm rock]

no

[orchid linden]

people just dont talk about it because slowdown -> less profit

[warm rock]

and no

[torpid cairn]

I think AI progress will slow such that each of us will have at least a chance of entering the job market, but it's still a big threat