Number Theory Help

[coral musk]

I am taking a number theory class and are stuck on this problem. I don't know where to start. Can someone help me?

[hazy dirge]

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[viral bay]

well, differentiate first.

we know that $1+\frac{dy}{dx}=0\implies\frac{dy}{dx}=-1$ for a minimum

[elfin nest]

dark matter

[coral musk]

what is the answer?

[viral bay]

i cannot tell you.

[coral musk]

oh ok

can you solve it without calculus

im not good at calc

how else could I start

[viral bay]

hmm, i don’t really know, tbh.

becuase then you would have to solve for y or x

and turn it into a diophantine equation somehow?

wait actually $(\sqrt{x}+\sqrt{y})^2=1183$

[coral musk]

yes

[viral bay]

implies that sqrt(xy) is an integer

[elfin nest]

dark matter

[coral musk]

it would be $x + 2*sqrt{(xy)} + y = 1183$

[viral bay]

yeah

[elfin nest]

chessnerd123

[coral musk]

what after that

[viral bay]

so xy is perfect square

all you have to do is $x+y=1183-2\sqrt{xy}$

[elfin nest]

dark matter

[viral bay]

yeah it makes sense now

[coral musk]

but how could you minimize x and y?

[viral bay]

oh min not max

hmm

[coral musk]

?

[coral musk]

how do you do it

[viral bay]

im working, sorry

[coral musk]

its fine

just tell me when you could give me a hint on how to solve

[coral musk]

@viral bay have you figured it out?

[coral musk]

those are positive integers

what are you doing

[coral musk]

start by simplifying the right hand side

1183 should be divisible by a square of some prime; try 7

[coral musk]

is help reqd @coral musk

I need help on a diff problem

I solved this one

oh

send it

[coral musk]

send the q and ill try to help

and if you have time also help on

[coral musk]

ah dang i havent done sums on like lists but i can do sets

[coral musk]

yea i can help ya with this

[coral musk]

💀 this aint sets but ig it involves it, wait ill try

ok sure

[coral musk]

can i consider that if i student is paired with a studentB that student cannot again be paired with another student?

[coral musk]

idk

everything you need to know is in the question

[coral musk]

im not able to solve it but ig u take permutations for this.

9900 permutations are there..

ok

if you cant solve that I have another one

[coral musk]

where do u even get these qs, but i like it, its challenging

so are all three of these questions requiring help?

[coral musk]

consider the maximum and minimum value that the median can take

[coral musk]

from my math coach

it is for MATHCOUNTS training

[coral musk]

i believe u take Sn first here

as long as it’s not the AMC10B

and technically

[coral musk]

yes

[coral musk]

why would it be?

my coach sent it to me

all big numbers shd be turned into - in order for it to be neg

oh mb

[coral musk]

they’re multiple choice questions sent at approximately the same time

u clear ur first doubt

[coral musk]

i’m being cautious, i suppose

[coral musk]

I got these problems a week ago tho

[coral musk]

note that at least one of x, y, z will lie outside [1, 7], and one of them will be the median

[coral musk]

would it be E?

[coral musk]

why?

[coral musk]

ans 15 for this?

bro dipped?

[coral musk]

btw one doubt, wht does ur status actually mean

you know The Game?

[coral musk]

nop..

[amber fossil]

Micabo don't

[coral musk]

why

[amber fossil]

it's for your good

[coral musk]

The Game is a movie

[amber fossil]

Yea sure

[coral musk]

?

[amber fossil]

just keep thinking that

[coral musk]

dw im the gay license agent for a reason

ill see wht he gonna do

https://en.wikipedia.org/wiki/The_Game_(mind_game)

or, if that’s too long,

~w the game

[shy cloak]

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Requested by micabo_l8r

[coral musk]

ok.

and

@amber fossil

[coral musk]

?

[amber fossil]

Ggs

[coral musk]

wht

[coral musk]

can u help me in a q i sent

[amber fossil]

Make a post

[coral musk]

i did

[amber fossil]

Send the link

[coral musk]

#1305782509677576242

i gotta eat

[cold mantle]

I got xy=(1183-x-y)2

Do some function stuff maybe and write the domain and range

MAYBE

a(x,y)=1183^(2)+x^(2)+y^(2)-2*1183 x-2.1183 y+x y

[coral musk]

he solved it.

[coral musk]

this gotta be 15

or at the least 14.

[lethal steppe]

@wise chasm

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[normal elbow]

minimum no. of minus signs are obtained when applied to the last terms

if its applied to say, L terms from the end

then S_(n-L) < S_l - S_n

given that Sn = sum (2n-1) = n^2