competition-math

[vivid ingot]

What about diabetes? 😔

[brave heron]

If eating 1 pack of m&m caused you diabetes, it's likely a you issue

[frosty pumice]

How would I go about rigorously justifying this? I was thinking planar graph but turning all curves into straight lines (moving nodes into a different dimension) but it doesn't sound very strong.

[cerulean ibex]

this probably belongs in #discrete-math

hint: consider the curve (r, r^2, r^3) for r in R

there are also ways to do this with topology, but strictly speaking no real topology is needed

[timber island]

Don't know about sleep chief but ill try

[cloud scaffold]

What comp
Do hard questions when doing revision
And check if they are right and if not see why you went wrong

[silk gazelle]

What is this

My friend said theres this

But i dont understand what and how this works

[ornate blade]

Fermat's little theorem

[royal estuary]

Nah

Thats the euler totient theorem

[ornate blade]

Oh right

[hardy jolt]

hyy guysss

Sorry to bother you, I wanted to ask. I have the intention of joining the Mathematics Olympiad but I'm confused about where to practice. Do you have any suggestions for websites/YouTube channels for practicing math questions, guys?

[thin shuttle]

As you raise an integer to a power, its remainder changes cyclically. For example, you have number 37. Its remainder by 11 is 4.

As you raise 37 to powers, the remainder will go like this:

4, 5, 9, 3, 1, 4, ...

Notice that when raised to 5th power, remainder became 1. We can use this to calculate 30th power.

37^30 = (37^5)^6 = 1^6 = 1 (mod 11)

So, hitting a remainder equal to 1 is very convenient.

There's a theorem that states that if youre looking for remainder of a^b divided by m, if m is prime, then a^(m-1) is guaranteed to have remainder 1. (unless a is divisible by m and has remainder 0 then, of course)

Let's apply this to our problem. We have m=11 which is prime, and 37 has remainder 4, not 0. So, we can apply the theorem, and obtain that 37^10 has remainder 1. (Without even having to manually raise it to a power!!)

So, 37^30 = (37^10)^3 = 1^3 = 1 (mod 11)

We got the same result.

[silk gazelle]

Thank you!

[autumn jackal]

Ok if you guys are so smart help me solve this

[royal estuary]

Gawd im in 8th grade

What is this

[autumn jackal]

Wizardly

[royal estuary]

Yeah right

[ornate blade]

maths for real men

[reef condor]

Trivial

If you are good

[shadow spruce]

Of course everything is trivial if you are good

[halcyon seal]

Lol

[terse canyon]

bro is tweaked rn

[slender barn]

seriously speaking though, what level math is that? im currently in 11th and it sounds just as wizardly so, but it looks damn intriguing 😭

[ornate blade]

graduate-level abstract algebra

a talented undergraduate student would be able to study this material however

[slender barn]

i see

it does sound really cool

[sour depot]

not a single number besides 0 T oT

[chrome quail]

I read this out loud and my fridge started floating

[sleek ravine]

bro asked to "solve" a proof 😔

[native ruin]

Is this a serious problem or just a bunch of bullshit you wrote after you got spanked by your drunk dad last night?

[royal estuary]

Yeah like i know uni level calc

But what was that

[ornate blade]

@royal estuary

[royal estuary]

Oh

Thanks

[shadow spruce]

Actually some Mathematical Competitions have topics of algebraic structure in high school level

[shadow spruce]

Real-Mathematics

[swift imp]

Cuz geometru is just like that 😭

[nimble nova]

knowing about the Carmichael Function can sometimes be helpful in contests. As its often a smaller number than Eulers Totient function so it leads to quicker calculations

[nimble nova]

you can view it as a "giga-totient function" and its defined as follows, for prime powers, the number 2, and the number 1, P^r -> Lambda(P^r) = P^(r-1)(P-1). For powers of 2 Lambda(P^r) = 2^(r-2). And for a number M with prime factorization N= p1^q1 p2^q2 ... pK^qK: Lambda(N) = LCM(Lambda(p1^q1), Lambda(p2^q2), ...) etc...

So we then have this nice result $a^{r} \mod n \equiv a^{r \mod \lambda(n)} \mod n$

[gilded halo]

frogeyedpeas

[nimble nova]

And more generally you can chain these. For example $a^{r^b} \mod n \equiv a^{r^b \mod \lambda(n)} \mod n \equiv a^{r^{b \mod \lambda(\lambda(n))} \mod \lambda(n)} \mod n$

[gilded halo]

frogeyedpeas

[nimble nova]

So an example if we were computing say $2^{{10}^{10}} \mod 37$ we first attempt to compute $10^{10} \mod 36$ and to do that we compute $10 \mod \lambda(36) \equiv 4 \mod 6$. So $10^{10} \mod 36 \equiv 10^4 \mod 36 \equiv (10^2)^2 \mod 36 \equiv (28)^2 \mod 36 \equiv 28$. And therefore $2^{{10}^{10}} \mod 37$ reduces to calculating $2^{28} \mod 37$ and that cna be done extremely quickly using modular exponentiation with squarings.

[gilded halo]

frogeyedpeas

[wraith bobcat]

37

[candid fern]

Hey, you can check my yt channel (little fermat) as I am uploading tutorial for math Olympiad topics

Here is a link: https://youtube.com/@littlefermat?si=IK9HxjCRxYXSr81g

[candid fern]

Also if anyone is interested in training for national math Olympiad contests, you can join the channel server here:
https://discord.gg/RcP9eX9yg2

[cerulean ibex]

ask mods b4 u advertise

[latent berry]

hi, just wanted to ask if anyone here has done the COMC? and if so, how did you study for it

[wanton badge]

Go to aops

[tall quartz]

Guys I need hint

[keen lake]

note that this is equivalent to ||1+n+n^2 | 1+n^3+...+n^2193||, then find ||the remainder when 1+n^3+...+n^2193 is divided by 1+n+n^2||, then ||bounding|| should finish

[buoyant arrow]

there is a +ve natural no. "n", find the sum of even numbers between n2 + n + 1 and n2 - n + 1

anyone pls help me

[modest marten]

hey yall

could you guys script some really hard AMC 10 level problems for me

to test my understanding

and push me

[thin shuttle]

Formula for arithmetic progression

[pallid tundra]

could you please find them yourself, thanks

[timid karma]

I assume you meant to write n^2? just a heads up for the future

[modest marten]

wtf is your problem

you didnt have to respond

[wanton badge]

Mind specifying which area nt , c or algebra

Also you can join mods server and look into prob with specific difficulty

[supple flame]

The number if positive integers x with x <= 60 such that each of the rational expressions 7x+1/2 , 7x+2/3 , 7x+3/4 , ... , 7x+300/301 is in the lowest terms (i.e. in each expression, the numerator and denominator have no common factors) is ?

[ivory ember]

I'm assuming you forgot to write parentheses around the numerators

Note that $\frac{7x+k}{k+1}-1=\frac{7x-1}{k+1}$

[gilded halo]

Civil Service Pigeon

[ivory ember]

and hence you just need to consider ||gcd(7x-1,n)=1 for n=2,3,...,301||

[sand hull]

Could you please find it yourself lazy ass?

[shadow spruce]

http://www.numberwonder.co.uk/ArnoldHagger/CNinGimo.pdf

[vague mauve]

could you find the solution

[radiant jasper]

<@&268886789983436800>

Don't make robloxians look bad bro

[brazen stirrup]

Yeah take X compact kahler 👍

[radiant jasper]

yaya

[ember ermine]

anyone know how hard this amc10 2025 will be to qualify compared to other amcs

ive been consistently qualifying for aime on older competitions and the latest one ive tried so far was 2018 where i qualed with like 10 point cushion

[willow anvil]

Hope not

[near apex]

😂 lol

[pallid tundra]

it's anyone's guess but prep for it as if it's gonna be balls to the wall hard

[austere wedge]

Are the AoPS books worth it if you wanna do competition math? They’re like 50 a pop and i only found like 4 of them on libgen

Just found two more nice

[ornate blade]

you have good libgen skills so just give it some more time lol

[shadow spruce]

So strict, more than 1 day late is 0

But if I’m actually really sick, and it is due tonight, possibly it’s better to do late submission or just simply don’t do it

[tame burrow]

Probably similar to the last few years

[ember ermine]

k

[radiant jasper]

does anybody have access to an amc 10/12/aime book that has a lot of practice problems

and i'd appreciate it if you could dm me the pdf

[silk spindle]

Does anyone have any advice for an eighth grader trying to take the amc 8 AND the amc 10 (first time taking both tests)

[untold thunder]

Unless you studied diligently, be prepared for a very hard test. If you want to prepare consider trying some of the past problem sets. Contrary to standard test taking strategy, you may want to consider not skipping over questions that stump you (on occasion) as preceding questions increase in difficulty.

[marble grove]

so you know like

AMC 8 and 10

or sum

are like majorly probability

bro for 3 years I have been calculating the probability by hand

so like

anyone know the formulas and when to apply them

[ashen jacinth]

yeh

[slender harbor]

i remember the AMC 8

[timber island]

Hey guys, wondering if you could help me with this problem
It's from an olympiad i recently went to and i got stuck because i've never dealt with exponential sums like this

[ocean narwhal]

Do you have the answer?

I got 12/(13*11)

Ill explain how if its correct

[timber island]

No, still have no idea how to get through this

[ocean narwhal]

well in short multiply the numerator and denominator by 12 to get rid of the i-1 in the exponent

then treat it like a normal telescoping sequence

[timber island]

How did you manage to get the telescoping sequence

[ocean narwhal]

like you got 12^i /(12^i + 1)(12^i + 12)

= 12^i/11 [ (12^i + 12) - (12^i + 1)]/[(12^i + 1)(12^i + 12)]

= 12^i/ 11 * [ 1/(12^i + 1) - 1/(12^i + 12)]

multiply the 12^i inside the bracket

youll see how it works out after that

[austere wedge]

aops is pretty good so far

[acoustic nova]

pay for them

[austere wedge]

Too poor, maybe later

[stark sequoia]

Just pirate them

[wary magnet]

AoPs would be a much bigger company if AoPs had better ways to stop pirating

[radiant jasper]

who cares

math isnt exclusive to the rich

[acoustic nova]

the books are not at all expensive for what they are worth

u should not pirate

[radiant jasper]

also im banned from editing the aops wiki

[acoustic nova]

why

[radiant jasper]

cuz i was trolling on the 2024 amc 10

page

[acoustic nova]

bruh

do something useful

[radiant jasper]

bro it was useful

i gave them a free mock test

25 problems of past amc 12

[wary magnet]

lmao

[pallid ginkgo]

any reccomendations for olympiads in aops? i like aime with how it doesent have alot of questions, but i feel like aime is slightly too high level for me

[pallid tundra]

try the later problems on AMC 10/12 and/or do some diving in the contest collections and see what you find

[tranquil spire]

I am very new to SEAMO questions. Should I just learn solutions along the way and analyze the structures of the questions?

Brain not braining rn, I need to study

[brave heron]

Is seamo even worth it?

I heard the regis fee is high

[tranquil spire]

very. The stuff in it doesn't seem very challenging imho

It seems to be ok. but honestly the regis is around 20 bucks or sth

[brittle remnant]

I was working on this problem but don't fully know how to do it

How would I find the lattice point with a limitation

[vagrant robin]

bro itz simple first try to observe any pattern

if not use telescopic method

[brittle remnant]

Can you elaborate please

[reef condor]

Catalan

[reef condor]

I think by telescopic they mean recursion

[brittle remnant]

Wouldn't catalan numbers only work if k=1?

[reef condor]

I meant to use it for inspiration

[brittle remnant]

I new to this type of math how would you go about solving it?

Becuase Im stuck

[brittle remnant]

How would you solve it though?

[sharp lake]

Recursion would make sense. I mean its like first thing that comes to my mind

Actually idk about that. Try solving for k = 1 , 2 , 3 and get the feel for this

[nimble valve]

1+1💀👽

[boreal sky]

Given $a,b\in\mathbb{N}$ such that $a\geqslant b$ such that $a^n+b^n\mid (ab)^n+1$ for all $n\in\mathbb{N}$, prove that $b=1$

[gilded halo]

Its_TheMathCraft

[brave heron]

20 bucks? I heard it's like 100 usd

[marble grove]

Junior international math olympiad

[tranquil pilot]

aops is bigger than ur mom kid

[soft vigil]

nah

aops has books

but the best part of aops for a lot of people is the forums

which are free

also aops has sponsorships from big companies

[radiant jasper]

try using AMC trivial to expand your knowledge

after solving a question given by AMC they give the solution to help you deepen your understanding

[loud gull]

I'm looking for problems that are easy to remember. For example, what are the last 2 digits of 3^3^3^3^3?

Another example: for what values of x>0 does x^x^x^x^x^... converge?

[azure bloom]

Bruh

Oh sorry that was many days ago that is just what Discord had me scrolled up to

[acoustic nova]

wdym easy to remember?

[scarlet hill]

holy moly

[radiant jasper]

how old is bro

dont think ur old enough to call other people "kid"

[plain tartan]

https://math.stackexchange.com/questions/4866392/if-anbnabn1-for-each-n-in-mathbbn-then-1-in-a-b

I think it can be done using the Euler theorem (similar to IMO 2024 p2)

[reef condor]

Bruh I remember this was kinda trivial in Otis

[boreal sky]

Thankyou sir

[graceful coyote]

Can someone suggest maths Olympiad for high school students

[radiant jasper]

if your starting off you should avoid doing speed/skill related Olympiads, e.g AMC, IMO, NMO, etc. start off with simple math olympiads like HKIMO, TIMO and PHIMO

[radiant jasper]

hmm, try this one, it looks hard but if you look at it with focus and intent you can easily solve it, its pretty easy but very tricky

just @ me if you want the solution and video explaining the solution

ill give an easier question if you cant solve it

[ornate blade]

HKIMO is just as hard as AMC if not harder btw

[radiant jasper]

ehh maybe

[ornate blade]

like AMC has the easy questions in the first half

[radiant jasper]

true²

[ornate blade]

avoiding AMC is kind of a recipe for failure if they want to start small imo

[radiant jasper]

2nd half it gets harder and harder

[radiant jasper]

real

[ornate blade]

cause a lot of other olympiads will never start off that easy, if you're excluding English speaking countries (Canada, Australia, UK etc)

HKIMO is more like a consistent level of hard in which all questions are fairly challenging and the last bit is also kinda impossible

I might be confusing it with other HK olympiads

[radiant jasper]

what HKIMO are you referring to

[ornate blade]

but there's one in Hong Kong where the first few are worth 5 points, the next are worth 6 points, and the last are worth 7 points or something

[radiant jasper]

hong kong international mathematical olympiad?

[ornate blade]

http://www.hongkongimo.com/

yep

[radiant jasper]

yeah

[ornate blade]

oh wait that other one is probably the AIMO or something

[radiant jasper]

thats the one in referring to too

[ornate blade]

https://www.hkmo.com.hk/contest/aimo.php

there's another one in Hong Kong

[radiant jasper]

honestly HKIMO heat round was quite easy

[ornate blade]

ah I see

[radiant jasper]

their entrance fee for the final round is just outrageous tho

100 dollars for a medal i can make for 10 bucks

[loud gull]

Another example of a problem that's easy to remember: How would you tile a floor that's 1999x1999, using tiles of size 4x6 and 5x7?
This is a set of easily-remembered problems.
https://jaymaron.com/fermi.html#cmath
It also helps if the problem looks cool, or answers a cool question.

Also seeking problems where you estimate a number, and the goal is accuracy. For example, what is the integral from 0 to pi of sin^32(x)?

[high goblet]

i'd argue this year's IMO P5 is quite a nice problem

it might be a little troll lol but it doesn't require too much background knowledge and is fairly easy to remember

[high goblet]

also another good one is

if n is a kth power modulo p for all primes p, must n be a kth power?

[brave heron]

I just know you are from ph

[brave heron]

Timo and Hkimo were simple compared to Phimo because they just put everything there, BBB on the other hand is really outrageous compared to the three

[radiant jasper]

vietnam*

I competed in TIMO and HKIMO during elementary school

thats why I know them

i dont know what BBB is tho

[charred sun]

I have an exam in 9 days, I am giving my learning objectives can anybody give me some tricky competition math problems you have done which test all the concepts so I am prepared for the tricky curveball questions since it has been 2 weeks since I have finished my learning objectives so here's the learning objectives

Statistics 1
Mathematical models in probability and statistics; representation and summary
of data; probability; correlation and regression; discrete random variables;
discrete distributions; the Normal distribution.

Pure 1+Pure 2
Proof by exhaustion, deduction and disproof by counter example ; algebra and functions - quadratics, indices, simultaneous equations, quadratic inequalities, graphs and transformations; coordinate geometry in the (x, y) circles plane;
sequences and series; exponentials and logarithms; trigonometry sin and cosine rule area of a triangle, radian measure, trigonometric graphs and identities and trig equations without the reciprocal functions the simple ones;
differentiation only 1st derivative and second just this equation nx^n-1 that's it stationary points maximum and minimum; integration only the first equation (x^n+1)/n+1 definite integration and area under curve and trapezium rule.

[loud gull]

Imagine more math contests in elementary school.
Could change the nature of school.
How did you feel at the time?
How can we inspire the next batch of kids?

In Texas, every elementary school kid knows that football is a path to upward mobility. They train hard. They dream of being in the next batch of Texas football stars.

[loud gull]

The Science Olympiad has leagues for high school, middle school, and elementary school.

[stray glacier]

Hello

Can someone help me with math

[ornate blade]

wouldn't it make kids more burnt out

also there's a lot of mental health impacts as well as physical ones in the NFL (specifically, concussions have led to a greater risk of Alzheimer's and dementia at a young age)

man elementary school kids just need to play and focus on school

gifted kids can be better served in other ways rather than competitions

[tranquil pilot]

sry i was half asleep lmao

[loud gull]

Rich topic of debate. Perhaps find a balance?

[ornate blade]

prolly

[loud gull]

Sports, music, math, science, history, english, playground, etc.

[graceful coyote]

Are these Olympiads good for building deep conceptual knowledge

[untold thunder]

In my opinion, I think their questions are creative and they can build this connection because you're required to think critically. IMO is extremely hard, AMC is intermediate, and I am not really sure about NMO. It's probably similar in structure to AMC, though.

[brave heron]

Big Bay Bei is part of the trio of TIMO BBB HKIMO, + PHIMO

[radiant jasper]

oh, ok

[radiant jasper]

NMO is short for NATIONAL MATHEMATICAL OLYMPIAD, i typed it because i dont know where he comes from, and NMO is more specific than MO

[radiant jasper]

Tbh if you really want to achieve in maths competitions, i would stay away from those olympiads

[radiant jasper]

if you're trying to get kids into math, just let them do a secret diagnostic test for whos good at math and whos not, while also making math more enjoyable for them

My motivation as a kid was just to join my country's math olympiad, mainly due to the cash prize

[radiant jasper]

it depends if the kid is gifted or not, thats why I said to let them take a diagnostic test to acknowledge their skills

[radiant jasper]

I cant consider IMO to be extremely hard, maybe hard and very tricky, you just have to look at the question intently and you'll get it, otherwise just wait for the answer to come to you, I answered prob 1 of IMO right before I went to bed, so I started writing my answer as fast as possible to not forget it.

[radiant jasper]

I think some IMO questions can be quite doable and others can just be drop dead hard

[modern prawn]

bruh i feel like gifted is kind of defined wrong in math

knowledge and being gifted is two different things

most “gifted” kids simply work hard/get forced to study

[radiant jasper]

I agree with that

[modern prawn]

or their parents put them in like 4 math classes a week. No wonder they’re good at math

I think that less than 1% of the population is truly “gifted” and even with that, unless you’re a prodigy, then it will take a lot of hard work to actually be good at math

I hate the fact that people think they can’t be a mathematician if they didn’t do calculus at 6 or isnt “gifted”

[radiant jasper]

Where I'm from, people stereotype us as being all "smart" and gifted but the reality is that we just do lots of extra math lessons

Idk calling someone gifted or smart would make others feel bad for not fitting the label as a "good student"

[grim forge]

in terms of “gifted” or who’s good at math or who isn’t, what really matters the most is how dedicated they can be into the subject - or any subject as for the matter.

with the right motivation, tutelage, discipline and rest, one can acheieve greater levels of math no matter what their level was originally

[modern prawn]

You see those kids that do college level math at like 10? Those are actual gifted kids. Otherwise, its all hard work basically

Nothing limits you from being a “genius” at math with enough hard work

[grim forge]

and even in other subjects as well

[modern prawn]

In math, it’s just the earlier you start, the more ahead and “gifted” you’ll be

At early ages its much easier to go fast and skip

Surely you can speed ahead subtraction and addition compared to algebra 1 or something

[radiant jasper]

i started integral calculus at 9 due to kumon and other stuff

[modern prawn]

💀

[radiant jasper]

kumon trauma

[modern prawn]

Thats definitely too early but I cant speak for you

Feel like theres no way your fundamentals would be developed enough for integral calculus at that point

[radiant jasper]

i forgot if it was integral calculus or normal calculus

probably normal

[radiant jasper]

Thats interesting because in my school, calculus isnt taught until Y12

[modern prawn]

Well, I’m only in algebra 3 (int algebra) so I can’t speak lol

Probably gonna take calculus in a few years

I don’t care about taking it fast or something I like math

[grim forge]

for me, AP calculus 1 was an elective class and i took it as a challenge for my senior year of high school (which was last year)

[radiant jasper]

it was probably normal calculus because if it was integral calculus i would be a master at it by now, but im still struggling

[modern prawn]

bro how did u get into calculus at 9 💀

[radiant jasper]

I did notice that in the US, they learn calc quite early on in school

[grim forge]

it’s a surprising fact to say the least

[modern prawn]

I don’t need to take calculus in school tbh

I can take ap calculus without school and still get cc

[radiant jasper]

started kumon at 3

kumon has like 12 levels

took me 1 year to get through level A and B

4 months for C and D

[grim forge]

there are enough resources regarding AP calc after all

[radiant jasper]

My asian trauma

and i forgot the rest

[modern prawn]

My dad and mom never forced me to do much academics

They don’t really care what level I’m in as long as I have good grades

[radiant jasper]

kumon has pretty basic stuff

[modern prawn]

I still have asian trauma from other things though 💀

[radiant jasper]

their yr 9 algebra is pre algebra

thats why i did it so fast

[modern prawn]

Schools need to shift their math down a grade level

I don’t want to sound pretentious but they overcompensate their math difficulty to accommodate for students who are behind tbh

[radiant jasper]

true

why give the same question to students at different levels

[modern prawn]

I can assure you most 7th graders who are average at math (in terms of school) could skip to algebra 1 and geometry and survive

[radiant jasper]

kumon forces you to start at grade 1, even if you're in highschool

[radiant jasper]

barely

[modern prawn]

Yeah, but they can survive

[radiant jasper]

yeah

[grim forge]

that’s genuine insanity

[modern prawn]

Geometry and algebra 1 are normally considered 9th grade

[radiant jasper]

what

[modern prawn]

So maybe those 7th graders can take geo and algebra 1 in 8th grade and survive

[radiant jasper]

i thought algebra 1 was 7th

[modern prawn]

yes

Its 2nd grade for asians

[grim forge]

quite frankly, i did algebra 1 in 8th grade

[modern prawn]

Algebra 1 is taken in 9th grade on a normal curriculum

[radiant jasper]

im asian

[modern prawn]

I hated math and sucked at it until middle 5th grade

[radiant jasper]

new knowledge

[modern prawn]

Then I started liking it

[radiant jasper]

relatable

the fact that it was starting to be mostly numbers and not "andy had 2 apples" made me start to like it

[radiant jasper]

Most of my olympiad papers have more letters than numbers I was going to flip

[radiant jasper]

I found problem 2 i think from IMO 2021 to be generally easy

it was just proof

Could I see

there

it looks hard but honestly its just tricky and annoying

[modern prawn]

Nvm you are genius 💀

[radiant jasper]

then after you solve it you say "ts is easy"

[radiant jasper]

dude no

check their IMO website

they have like 3 steps in solving it

[modern prawn]

Making me feel dumb bruh

[radiant jasper]

shi solution was longer than i remembered

i swear it was short for me

[modern prawn]

I have no idea what the hell is going on

[grim forge]

i’m guessing this is related to linear algebra (in a sense)

[radiant jasper]

me neither

[modern prawn]

Calculus is probably not for me 💀

[radiant jasper]

they over complicated it

[modern prawn]

I mean IMO is high school math

But hard

[grim forge]

?!

[radiant jasper]

i think its a mix of college and hs math

[grim forge]

i thought it was university math

[modern prawn]

No, it has no college level math

Well

[radiant jasper]

college like pigeonhole, chinese remainder theorem, etc

[modern prawn]

You can solve it using college level math

But its mainly high school curriculum but insanely deep

[radiant jasper]

i forgot if pigeonhole was taught in college or hs

[modern prawn]

Its a high school math competition

[grim forge]

we can bet it’s college knowing that’s a part of stats

[modern prawn]

Pigeonhole is something i learned in algebra 2 wdym

Is it a different thing

[radiant jasper]

its combinatorics

[radiant jasper]

statistics*

[modern prawn]

not that

[radiant jasper]

CRT 💀

[modern prawn]

I suck at combinatorics

[radiant jasper]

CRT was so hard for me to understand before

[modern prawn]

what the heck is crt

[radiant jasper]

Chinese Remainder Theorem

anything with modular arithmetic i give up

[radiant jasper]

real

modular arithmetic is so easy yet so annoying

Yeah

you have to do so many cases

like all the manipulations

case 1: the ball went into the toilet and then due to that caused a tsunami from Afghanistan which also caused the ebola virus to spread worldwide

Fermats Little, Eulers toitent, Wilsons, CRT, Hensels Lemma .....

[radiant jasper]

basically mod arithmetic in short

[radiant jasper]

Euler's totient was also pretty annoying but easy

[radiant jasper]

yeah

I felt like when i saw the Toitent function formula i thought it was hard

but its actually rlly easy

[radiant jasper]

yeah, but when you understand its really easy

the formula just has a lot of symbols thats why

[grim forge]

when do you learn euler’s toitent formula?

[radiant jasper]

college i think

but you can learn it at 5th grade

[radiant jasper]

but its used alot in competions

Yeah its just prime factors

[radiant jasper]

and fractions

[modern prawn]

Stop speaking alien

[radiant jasper]

Yeah but it really isnt that bad compared to CRT

[modern prawn]

I don’t understand anything lol

[radiant jasper]

zibzab

[radiant jasper]

crt is hell

Yes

I agree

[radiant jasper]

Enjoy

[modern prawn]

I mean doesn’t look that bad

[radiant jasper]

let me give you an elementary CRT problem 😭

[modern prawn]

It seems like normal modular arithmetic but harder

[modern prawn]

PLEASE NO

[radiant jasper]

but CRT 💀

[modern prawn]

wait i actually wanna see

I wanna see how much CRT or whatever makes my brain implode

[radiant jasper]

couldn't find it

HKIMO hides their past papers too well

[modern prawn]

isn’t this normal modular arithmetic

[radiant jasper]

and I'll get arrested for pirating them

[modern prawn]

You did imo?

Bruh 💀

[radiant jasper]

IKR 💀

[radiant jasper]

HKIMO means hong kong international mathematical olympiad

I cannot find any of them

or AIMO

[modern prawn]

Aka imo

[radiant jasper]

or IJMO

its not the same as IMO

IMO is hard

HKIMO is tricky

[radiant jasper]

IMO is the big boss of maths olympiad

[modern prawn]

My self confidence is declining every second I’m in this chat

[radiant jasper]

everyone here has 0 self confidence

[modern prawn]

I understood about 2 words in the past 10 minutes 💀

[radiant jasper]

Modular arithmetic isnt actually hard

its just CRT

that kills ppl

Its so long and tedious

Every time I answer a question during a math olympiad i say ( not sure) to not humiliate myself for being too confident

[modern prawn]

Man

I can barely even make aime qualifier idk why im here

💀

[radiant jasper]

whats AIME

[modern prawn]

its part of amc comps

[radiant jasper]

just use AoPS (site) and AoPS vol 1 and 2 (books)

[modern prawn]

Its what you get into for top 2.5% in amc 10 and top 5% for amc 12

[radiant jasper]

and you'll be fine

[modern prawn]

Wha-

There. Is. A. Volume. 2?

[radiant jasper]

yes

[modern prawn]

Dude I’ve been using aops for a while

HOW DID I NOT EVER KNOW

[radiant jasper]

Art of problem solving: volume 2, and beyond

The basics = vol 1
And beyond = vol 2

[radiant jasper]

use the site as well and watch numberphile

[modern prawn]

I’ll ask my dad for them lol

Feel like book alone is worse than the aops classes though

Whatever idec

Gimme that volume 2

[radiant jasper]

volume isnt that bad

wait i also have a book to recommend

[modern prawn]

thank u my beloved

[radiant jasper]

The art and craft of problem solving by paul zeinittz

idk how to spell his last name

[modern prawn]

This conversation gave me humility. I now feel like 10x more of a dummy

[brave heron]

*CMO

[brave heron]

In my case, it's a really decent pasttime and decent training for some basic math knowledge, + theres not a lot of competitions in my country, I don't think they did the AMC this year so we are cooked

Anyone knows when are they doing ICO?

[brave heron]

And actually a lot of the IMO participants or somewhat part of the IMO camp joined these as a starter and improved

In my country

[radiant jasper]

nah

IMO has harder questions in particular

[radiant jasper]

my opinion

[high goblet]

i'm assuming CMO refers to china's maths olympiad

whilst the IMO is generally 'the last' goal for a maths olympiad contestant

the TSTs for some very high scoring countries tends to be harder than IMO

i.e. USA, China

[past surge]

Hello, I'm a high Schooler and I'm very interested in improving my math capabilities. Right now I'm in calculus and the biggest issue I have is information retention, I've done amazing in math, grade-wise, but for some reason the info never sticks. I don't think my study methods are beneficial. They're good for short-term success but for long-term comprehension, they're obsolete. Does anyone have any study tips for me to improve my study methods and build my mathematical skill?

sorry if I typed this in the wrong channel, but ya'll are comp math so I assumed you'd have some great advice.

[modern prawn]

As a person who’s worse than you at math, and probably have nothing good to say, you’re probably relying on memorization based techniques instead of actually intuitively understanding the subject

I feel like it would be easier to help if you listed your current study methods

Rote memorization will most of the time end up with you forgetting it

[sinful mountain]

*putnam

[ornate blade]

*China TST

[loud gull]

Is there a contest with calc and differential equations and complex analysis, but not higher stuff like real analysis and group theory?

Or a contest with just calculus and not beyond? You need calculus for cool questions, and for continuum math. Most contests are heavy on discrete math.

[radiant jasper]

wait true

[ornate blade]

I mean I was joking, no one would think that Putnam would be easier

[novel karma]

dam this is the most active this channel has been in a while

@modern prawn also do you speedcube? js curious

[modern prawn]

Yes

[novel karma]

oh same!

how fast your avg and pb?

3x3

[modern prawn]

i avg 10 seconds

pb single i dont know idrc about it but its somewhere around 6.3

[novel karma]

talk in dms we can't go off comp math here lol

[untold thunder]

Does anyone know how many hours per day and for how many days it would take a person with basic comp. math experience to AMC 10 level?

[brave heron]

I solved like atleast 10 of them already, while i'm trying to solve 2 from the CMO TST

Such a shame that the top of this years CMO got silver at the IMO(partially because of P5)

[brave heron]

Not fair, putnam is for college students

[brave heron]

Tbh the best way for info to stick inside your mind, is to do a bunch of practice problemd to the point it's just basic common sense

[marble grove]

guys help

∀2m ∃p1,p2 : 2m = p1+p2, m ∈ ℕ

my coach told me this is a nez problem

and that even a 9th grader who scored a 20 on AMC 8 could solve it

[modern prawn]

It depends

Knowledge and problem solving are two different things

Someone in ap calculus AB could struggle in amc 8, and maybe only get a 20.

School math is primarily knowledge. Comp math is primarily problem solving

I mean

Its easier when you know what the symbols mean

[modern prawn]

how do you get a coach 😭

they’re so expensive

[marble grove]

school coach

[marble grove]

I know a couple indians around the block

[modern prawn]

Sch-

Your school has math like that?

Bruuuuuuuhhh

[marble grove]

it was a joke lol

[modern prawn]

phew

[marble grove]

its goldback's conjecture

[modern prawn]

Every indian child has 24/7 math coaching

[marble grove]

fr

bruh

like fr tho what is an upside down a

[modern prawn]

I have no idea. From what I searched up, it means “For all”

[marble grove]

bruh we both lost

[modern prawn]

I am not as good as you in comp math. I’m literally a 95 ish AMC 10

[marble grove]

is that good

[modern prawn]

no

[marble grove]

thats 5 points away from 100

[radiant jasper]

its out of 150

[modern prawn]

the max score is 150

[marble grove]

bro i think i got like a 40

[radiant jasper]

not possible

[marble grove]

idk then

[modern prawn]

If you dont answer anything

You get a 37.5

[marble grove]

but i calculated all the probability ones by hand 😭

just rawdogged it

o

[modern prawn]

did u take the amc 10

[marble grove]

alr oogabooga

uhm i think

i scored decent maybe on amc 8 so they took me to do amc10

[radiant jasper]

how do you not know

[modern prawn]

my amc 8 is like 19

[marble grove]

bro that was freaking 1 year ago

i got a 24 or 25

[radiant jasper]

bruh

[radiant jasper]

nice

[modern prawn]

dude i told you

[marble grove]

wait no

[modern prawn]

im trash

[radiant jasper]

19 is still distinction honor roll riht

[marble grove]

idk tho

bro my freaking friend

got an 18

as a 6th grader 💀

[modern prawn]

yeah normal in my school

[radiant jasper]

thats pretty good

[modern prawn]

in my school a 6th grader got a 25

[marble grove]

i could have def scored higher if i knew formulas

[modern prawn]

dude what

amc 8 barely has much formula except c+probability

[radiant jasper]

no

you have to know how to apply them

[marble grove]

yeah formula for probability

[radiant jasper]

?

[marble grove]

the problem was for the probability and the other ones i guessed and checked

[radiant jasper]

bthu

[marble grove]

and i ran out of time and rushed the last like 7 questions

[radiant jasper]

bruh'

[marble grove]

ok but to my defence i got no training or anything

[radiant jasper]

tbh for amc 8 the only one you need is like stars and bars

or sticks and stones

or balls and urns

or ones and zeros

[marble grove]

sticks and stones may break my bones

[radiant jasper]

or dots and dividers

[marble grove]

idk what bro is on abt

[radiant jasper]

different names for stars and bars

[marble grove]

o

but like

i might study for amc 10

[modern prawn]

this time im hoping to get 110 for amc 10

prob not though

[marble grove]

and then do medium on amc 12

[modern prawn]

bruh

amc 10 and 12 is basically the same thing

but amc 12 has trig and its a slightly harder version

same type of problems though

[marble grove]

im decent at trig

like soh cah toa fr

[radiant jasper]

u can do it

[modern prawn]

you think you’re decent at trig until you see math comp trig

[marble grove]

like

[modern prawn]

normal school trig is hard to apply in math comps unless you’re really good with geometry foundations

[marble grove]

i could do that

fr

[modern prawn]

hvm

you’re smart as hell

[radiant jasper]

trig bashing

[radiant jasper]

fire

soh cah toa on repeat

[marble grove]

btw i found that on the internet bruh

it would lowkey be fun if those were group events

[radiant jasper]

lmao this is coord bashable

[modern prawn]

I wish more people in comps actually enjoyed math

I can bet you 40%+ of people in comps got forced to by their parents and don’t actually like it

[radiant jasper]

i like it

[marble grove]

I enjoy math until my friend bashes me cuz he is smarter lol

idk abt the math community

[modern prawn]

amc 10 goated

aime is too hard

I dont understand crap

look i would prefer problems to be in words not in scribbles

[marble grove]

oh

my friend is tryna make

JIMA

[modern prawn]

wat JIMA

[marble grove]

its like

[radiant jasper]

jmo?

[marble grove]

junior international math olympiad

or something

or it might have been national idk

[radiant jasper]

ijmo?

that's boring lmao

[marble grove]

random pics

[radiant jasper]

imo?

[marble grove]

the guy is always so serious lol

yeah ijmo

and then he is trying to do imo b ysenior year or sum

idk how tohe competitions work tho

[modern prawn]

i thought it was usajmo

oh wait

thats different

im dumb

[radiant jasper]

Was it the one is Bali last year

my math teacher is raging about american school system

[marble grove]

i forgor prolly tho

[shrewd girder]

I could be wrong but im pretty sure the first pic that cat22 posted is like almost a decade old

idk about the second

and that its IMO

yeah lmfao i was right

https://www.deseret.com/2015/7/22/20568678/u-s-wins-international-math-olympiad-for-first-time-in-21-years/

didn't know that the US didn't get a single win for 21 years before 2015 though damn

is that even true

i dont think so actually

[radiant jasper]

I can solve like 15 CMO problems, + the reason for CMO is eliminations for IMO

[radiant jasper]

Putnam is easier than IMO, its the fact that Putnam has a broader range of math topics than IMO

[radiant jasper]

go to help

[radiant jasper]

not really, if you just look at it for some time you'll probably get the answer

[shrewd girder]

ehh i would say usually the first few problems on the putnam are definitively easier than IMO but as you go further they become pretty comparable

altogether im not sure though, i think we would need to compare how much time you can allocate to each question as well

[radiant jasper]

IMO questions are still harder in my opinion tho

putnam just has a wider range

[shrewd girder]

ah ig if youre excluding like the difficulty that gets added with the amount of underlying concepts then i agree

[radiant jasper]

"Team USA edges China, drawing comparisons to 1980 Miracle on Ice Hockey victory over the Soviet Union."

[radiant jasper]

putnam is harder

[radiant jasper]

ive heard IMO gold medalists say IMO is harder, while Putnam is also hard

i mean the first few problems are A LOT easier on the putnam

[radiant jasper]

harder to score perfect on putnam

[radiant jasper]

so just because this guy said that the putnam is easier means that everyone will think the same way?

[jovial coral]

We also can't sub out the fact it may be a lie

[shrewd girder]

yeah although i've heard that opinion before as well but the reasoning given was due to the time constraints

you only get 30 mins on average for each question on the putnam cause its 6 hrs for 12 questions

like its plausible that you blow past the first few in less time and that number is higher for the rest of the problems but iirc it still is substantially less per problem than IMO

[modern prawn]

Yeahh… no.

[pallid tundra]

fun fact: way back in middle school i competed against one of the 2024 IMO team members in MATHCOUNTS

[modern prawn]

bro how

[ornate blade]

scanning this chat rn to see if Luke Robitaille is hiding

lol

[pallid tundra]

jordan lefkowitz moment

(I went to middle and high school in CT)

[ornate blade]

oh wow

jacked

[pallid tundra]

and the even funnier thing is

now I help run a HS math contest at my uni

last fall our winner

also went on to win IMO gold this summer

🤠

bro was smurfing HARD

and easily got a perfect score on our contest

[radiant jasper]

sorry sent it to the wrong server

just noticed rn

[winter sable]

i am new in this competition

anybody wanna compete? i m in 9th

@everyone

[radiant jasper]

Same, just started 9th

[winter sable]

Cool

What chapters you on

[modern prawn]

Wdym compete?

[winter sable]

lets see who can solve hard problems

[modern prawn]

Oh, Im not that good, can you tell me your background

Just wanna see how good you are so I can see how hard I’ll be clapped

@winter sable

[winter sable]

i am in 9th standard i have completed my book , i know some basics of trigonometry , logarithms , permutations , inequalities

[modern prawn]

ok i think you’re slightly better

actually

[winter sable]

i m gonna start calculus soon

[modern prawn]

nah we probably equal

nvm

wh

[winter sable]

hehehe

[modern prawn]

how do u only know the basics of trig and starting calculus

[winter sable]

i am doing trigonometry still..on the process

[modern prawn]

wanna do this in dms

[winter sable]

stop being freaky bro

[modern prawn]

what’d i do

💀

ok fine

no trig i suck at it

[winter sable]

lmao

what standad u on

dard*

Derd*

[modern prawn]

uh i know as much as an algebra 2 student

[winter sable]

wdym by that

are u indian?

[modern prawn]

ok just give problem

no

[winter sable]

then?

[modern prawn]

im in an algebra 2 class

[winter sable]

alr..but tommorow its already 10:30 pm

[winter sable]

which country

[modern prawn]

america

[winter sable]

nd whats an algebra 2 class?

[modern prawn]

im not good at math

its the second year of algebra, usually taken before or with trig

[winter sable]

a 7th standard kid of india can easily clear sat's of amr

[winter sable]

oh..you got so much divisions in maths?

[modern prawn]

so you’re indian?

[winter sable]

yeah

algebra is a single chapter in indian books

[modern prawn]

no

algebra 1 is a full year course in america idk how u would teach it in a few pages

[winter sable]

we do a whole book including a variety of chapters up here..whose levels increase as you go in higher classes

[winter sable]

oh lol..so what youve learnt till now?

[modern prawn]

i can show you in algebra 2 questions

[winter sable]

kk

[modern prawn]

to show you overall difficulty

[winter sable]

yay

okk

you guys go to college after 10th?

[modern prawn]

no

[winter sable]

damn

never heard of terms like foci and direction in algebra lol

[modern prawn]

I hav no idea how to do this btw, like 1 chapter away from this

[winter sable]

OOOO

[modern prawn]

i told you

[winter sable]

i have done cp\onic..

[south cliff]

anyone doing the UKMT senior tomorrow?

[winter sable]

conic

[modern prawn]

i’m not good

[winter sable]

hyperbola , parabola nd stuffs

[winter sable]

i am indian

[winter sable]

whats yo age

[modern prawn]

13

[winter sable]

damn

i m 14

[south cliff]

fair enough I bet you do stuff harder than what is on that test anyways

[winter sable]

you guys learn only one topic the whole year?

[modern prawn]

no

[winter sable]

ikrr

[modern prawn]

algebra 1 is like a bunch of topics into one course

[winter sable]

summing all that up..there's only one topic then..algebra

[modern prawn]

algebra 2 also teaches basic trig

[winter sable]

thats so lame af

[modern prawn]

no

[winter sable]

Oh

[modern prawn]

?in algebra 1 and 2 there are 16+ chapters each

i’ll show u the trig alg 2 teaches

[winter sable]

did you ever do real numbers ...unitary methods..surface area ..circles..quadrilaterals

[modern prawn]

thats algebra 1

[winter sable]

send the syllabus freaky ghost

[winter sable]

OHHH

cool\

[modern prawn]

no

thats actually pre algebra

[winter sable]

oooo

can you send some questions

of pre algebra if possible..

[modern prawn]

pre algebra is really easy

its what 6th graders are taught

[winter sable]

oh lol

then

wait

i will give you one easy one

based on your pre algebra

ready?

[modern prawn]

the kind of trig alg 2 teaches

its not complicated trig its basic

[winter sable]

cool

yea

[modern prawn]

full trig teaches more

[modern prawn]

ok

[winter sable]

if x^2 + 1/ x^2 = 66 , find the value of x - 1/x

no cheating sir..

[modern prawn]

yea thats algebra 1 stuff

[winter sable]

^2 means squared

[winter sable]

do it

[modern prawn]

mannn ok

[winter sable]

hehehhe

[modern prawn]

i feel like i recognize this problem

did you get this from the sat or something

[winter sable]

idk abt that

i dont check sat questions

its from my book named rd sharma

do it man

[modern prawn]

oh lol

getting my notebook

[winter sable]

a lkg can do it faster

[modern prawn]

ok

i never said im good at math

[winter sable]

😭

ok take yo time s==igmer

10! sec

@south cliff you done?

@modern prawn *

[south cliff]

?

[modern prawn]

wrong ping 💀

[winter sable]

can you solve that question freak

[south cliff]

which one

the last picture?

[winter sable]

that doesnt matter , maths matters

[winter sable]

if x^2 + 1/ x^2 = 66 , find the value of x - 1/x

[south cliff]

which number?

[winter sable]

this one

[modern prawn]

im assuming its 66x, not sure though

im trash at math

i’ve been doing a lot of math comp practice and forgot how to do algebra 💀

wait

do you mean

everything over x^2

or only the 1

omg that makes it way easier

wat

i searched up the answer to the problem, got +8 with video solution and basically cheated, then checked with websites + video and it said +-8 whut, idk how that would work, because principal square root is positive only but whatever. I already searched up the solution (since u didnt respond), welp this was a wakeup call needed to cheat for an algebra 1 problem, been focusing too much on comp math i guess

[south cliff]

checking through ai is kinda cheating -.-

[modern prawn]

yeah true

i kinda cheated i guess

thats basically searching the answer up

[south cliff]

also

I dont think it can be -8 as well

[modern prawn]

this is wake up call to focus on algebra more after the comp happens

[south cliff]

im not so sure on that I cba figuring it out

[high goblet]

gl!

[south cliff]

you too! thats if you are doing it as well

[high goblet]

i'm not lol

unfortunately i am at uni now so i can't do any more UKMT competitions

i do mark the olympiads tho

[south cliff]

daaamn

I'm only pushing for a gold people getting any higher are gods

[high goblet]

ahaha gold is already really good!

[south cliff]

i got 67 last year and I havent revised much more

[ornate blade]

that's such a flex

[south cliff]

its just I did some revision for the MAT which kinda helps I guess?

[high goblet]

aha ty

[high goblet]

yeah that'll help

r u doing the MAT this year then?

[south cliff]

yeh 😭

[high goblet]

gl on that too!

[ornate blade]

you wanna get into Oxford right

[high goblet]

r u applying ox then? or cam?

[south cliff]

I'm applying just in case I get in you never know

[ornate blade]

Cam uses STEP right instead of MAT

[high goblet]

yep

[ornate blade]

I know you can use MAT for Imperial

[high goblet]

but some other UK unis give reduced offers if u have a good MAT score

[ornate blade]

but like most people aren't taking MAT for Imperial ykwim

[south cliff]

nah my options are like Oxford bath manchester leeds and liverpool

[south cliff]

by good im guessing like 70+ right?

I havent even attempted the big questions yet i've focused on the smaller questions too much

im so done for

[ornate blade]

which degree by the way?

[south cliff]

g100 I think?

[ornate blade]

I'll look up the UCAS code

sounds super familiar like maths I think

[south cliff]

I think I kind of just searched up maths

I didnt want to do anything other than that

soo

[ornate blade]

ah yeah BSC maths

[ornate blade]

makes sense

[south cliff]

I'm gonna do everything in my power to have a better chance at getting in I even will play the immigrant card 🙂

deprived area card also coming out fo sure

[high goblet]

i think it was like ~60+?

[ornate blade]

why the UK and not say the US, by the way?

[south cliff]

damn thats craazy

[ornate blade]

like cause of the cost or something?

[south cliff]

well we moved because there is better pay here and my parents couldn't find a job in italy which was where i lived for 10 years

[high goblet]

@ornate blade r u bri'ish?

[south cliff]

• our cousins live here so they helped out

[ornate blade]

nope

[high goblet]

damn

u seem to know quite a bit about uk unis lol

[ornate blade]

ah makes sense, io cognosco

[ornate blade]

well I spend time in the IB server and there's an active college-uni channel over there

so over time I picked up the bits of a lot of countries' application systems

mostly Western countries though

[high goblet]

ah ic fairs

[ornate blade]

I wouldn't know how it would be like to study at a UK uni though

🇦🇺

[high goblet]

yeah i generally find quite a lot of ppl in the UK tend to stay in the UK for university

esp. cus the UK doesn't really have a lack of good unis

[ornate blade]

absolutely it's just easier

[distant crater]

Anyone who has any tricks to solve 2^23 mod 83 without a calculator

[fast coral]

Just do 2^10 mod 83

[distant crater]

Why can we do that?

What happens with 2^13 then

[fast coral]

its just r^2 *8 mod 83

r = 1024 mod 83

[fast coral]

u can do that too

i just picked something easy

[distant crater]

I dont think i understand

[fast coral]

2^23= 2^10* 2^10 *8

2^10 is possibly common knowledge

1024 divide it by 83

get a remainder

so ur answer is the remainder * remainder *8

and if it crosses 83 divide it by 83 again

[distant crater]

Thank u! I think i understand now

[radiant jasper]

orz

[rancid beacon]

Can someone help me explain the solution? I don't get why it's y and 1/y....

[winter sable]

Sorry guys I slept

And ghost your answer is right

But you took a lot of time

[junior depot]

chat i have the same book💀

also do yall know what MMATHS is

if so pls tell me

[latent bough]

so basically if you plug ( sqrt( 3 + 2sqrt(2) )^x into 1/y and then rationalize denom, u end up with one as denom and (sqrt ( 3 - 2sqrt(2) )^x
i think

let me remember how to do the latex

,tex $$ \frac{1}{y} = \frac{1}{(\sqrt{3+2\sqrt{2}})^x} $$

[gilded halo]

reaver

[latent bough]

and you have to rationalize the denominator right

,tex \text{ so you multiply by $$ (\sqrt{3-2\sqrt{2}})^x $$ } \text { in order to rationalize the denom}

[gilded halo]

reaver

\text{ so you multiply by $$ (\sqrt{3-2\sqrt{2}})^x $$ } \text { in order to rationalize the denom}
```Compilation error:```! Missing $ inserted.
<inserted text> 
                $
l.49 ...multiply by $$ (\sqrt{3-2\sqrt{2}})^x $$ }
                                                   \text { in order to ratio...
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.```

[latent bough]

,tex \text{and that gives you $$ (\sqrt{3+2\sqrt{2}})^x * (\sqrt{3-2\sqrt{2}})^x $$}

[gilded halo]

reaver
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[latent bough]

,tex \text{which can be simplified to $$(\sqrt{3+2\sqrt{2}} * \sqrt{3-2\sqrt{2}})^x$$}

[gilded halo]

reaver
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[latent bough]

,tex \text{and then $$(\sqrt{(3+2\sqrt{2})(3-2\sqrt{2})})^x$$}

[gilded halo]

reaver
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[latent bough]

,tex \text{and you multiply out to get $$9-6\sqrt{2}+6\sqrt[2}-8 = 1$$}

[gilded halo]

reaver
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[latent bough]

,tex \text{so then $$(\sqrt{1})^x$$}

[gilded halo]

reaver
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[latent bough]

which is just 1 as the denominator

,tex \text{so it's just $$ \frac{(\sqrt{3-2\sqrt{2}})^x}{1} $$ $$= (\sqrt{3-2\sqrt{2} })^x} $$

[gilded halo]

reaver
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[latent bough]

supposes to be the whole thing over 1 but whatever

sorry for the slightly confusing explanation

[radiant jasper]

https://tenor.com/view/bumble-bee-sus-gif-8566306001639863160

[rancid beacon]

Crazy send me studying help plz

[rancid beacon]

Nah thank you though
So my book was wrong? It said something else

I'll watch some YouTube, hopefully get it

[latent bough]

they probably have a diff explanation i kind of reversed engineered to prove its right

[snow tartan]

Smc toooday

[winter sable]

Hi guys I m sigma

[ocean narwhal]

@maiden beacon let the fight begin

[winter sable]

Yay

Come on

[ripe iron]

How to calculate 1!(1²+1+1)+2!(2²+2+1)+...+n!(n²+n+1) ?
https://www.wolframalpha.com/input?i=1!(1²%2B1%2B1)%2B2!(2²%2B2%2B1)%2B...%2Bn!(n²%2Bn%2B1)
wolfram alpha says it gives n!(n+1)²-1 but how to arrive at this without wolframalpha?

[sacred hornet]

hint: ||telescope||

[ripe iron]

teach me the technique please

[sacred hornet]

that would spoil the answer, would you want that?

[ripe iron]

yes because I  don't know how to turn it into a telescoping sum

[ornate blade]

note that $(k^2 + k + 1) k! = ((k + 1)^2 - k) k! = (k + 1)(k + 1)! - k k!$

[gilded halo]

higher's secret twin brother

[ripe iron]

Ok, let me see

[sacred hornet]

oh i did it wrong

yea i had a minor mistake, but the telescope idea is right

[sacred hornet]

wait no i was right ur wrong

[ornate blade]

no, this is correct

[sacred hornet]

the end shud be $k!(k+1)^2-(k-1)!k^2$?

[gilded halo]

MartinFTW

[sacred hornet]

or am i not braining

[ornate blade]

if you telescope you get nth term - 1st term = $(n + 1)(n + 1)! - 1$

https://www.wolframalpha.com/input?i=sum+(k^2+%2B+k+%2B+1)+k!+from+k+%3D+1+to+n

[gilded halo]

higher's secret twin brother

[sacred hornet]

ohh nvm yea i get it both works

[ornate blade]

ah yeah it simplifies right

[sacred hornet]

i absorbed the term in factorial into the square

however, i still did it wrong the first go

but anyway yea i honestly dont have any "tips and tricks" for how to see telescopes you kinda just do and find out

[ornate blade]

hmm, $(k - 1)! (k(k + 1)^2 - k^2) = (k - 1)! (k^3 + 2k^2 + k - k^2)$

$= (k - 1)! k (k^2 + 2k + 1) = (k - 1)! k (k + 1)(k + 1) = (k + 1)! (k + 1)$

[gilded halo]

higher's secret twin brother

[sacred hornet]

its probably the same considering both answers are right

just the telescope term looks wonky