A functional equation from the 2002 IMO shortlist

#IMO​ #FunctionalEquations​ #MathOlympiad​
In this video we discuss a problem from the IMO shortlist 2002 in which we demonstrate some cool properties of surjectivity!..
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I upload videos concerning math Olympiad contests to help students preparing for math Olympiad and all people who share the love for some interesting math problems.
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[CreativeMathProblems]

Also, i believe the "trap" you talk about in your videos (where f is either one function or another) is called "point-wise trap". I saw this on a functional equation handout.

[gracjanworonowicz]

Very cool problem and clever solution!! I really enjoyed it!

[troxexlot]

Being surjective means all of domain is mapped but doesn't imply all range is mapped onto
still works since f(0) - 2x we have x= f(0)/2 as solution

[sahilaryal]

Excellent video again! Continue your work man.

[tiennguyenthibao]

Your videos regarding functional equations are so helpful that I watched them in one sitting. Hope you could do it with sequences :>>>>

[James-ygb]

can we substitute （0，y）after we prove f is surjective and get f（x）=x+f（0）

[bebarshossny]

thanks a lot for the video bro
please make more videos on the circle method since its a bit tricky

[James-ygb]

I have a question，can we substitute（0，y）into equation after we prove f is surjective and get f（x）=x+f（0）？

[abhipriyeshukla]

Bro I love u ur videos r very very helpful ❤❤

[yashvardhan]

Nice video
I saw one on sir Michael Penn's channel as well which used the fact.
It was from the Japan mathematical olympiad I think.
Plz make more videos.
Wanted to ask, were u yourself a medallist in the olympiads or participated in them.??

[comingshoon]

en las olimpiadas son comunes estos problemas ... saludos desde Chile brooo🇨🇱

[senjougahara]

Are you considering making a Geo series after this FE stuff? Good video btw :)

[yashvardhan]

Hello I am a viewer of ur channel.
Today I came up with a question
Find all n such that n!+n^2+2 is a prime .
Initially I framed this question for n being a prime but it was easy so I decided to generalise for all positive integers n but could only make out that n is 3 mod 6 . I tested certain values of n till 81 and found only 3, 15, 21 to be solutions but I cannot be certain.Are there infinitely many primes as the expression is 11 mod 36 for n>8 so by Dirichlets theorem maybe as gcd(36, 11)=1
Plz I request u to help me since my teachers too are not that good at Number theory .
Plz help .🙏

[CreativeMathProblems]

I like the design on the thumbnail, how did you make it? I wanna make such thumbnails too

[prod_EYES]

I got f(x) = x+1, I only started learning functional equations today.

[sohilaryal]

Good job!
Hey could you help me solve this problem?
Find functn fR+--R+ such that
f(x+y+f(y))=x+2f(y)