GCD of Polynomials | Number Theory | Korea Junior Math Olympiad 2012 Q4

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#NumberTheory #Polynomials #MathOlympiad

I share maths problems and maths topics from well-known contests, exams and also from viewers around the world. Apart from sharing solutions to these problems, I also share my intuitions and first thoughts when I tried to solve these problems.

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Seeing 43 = -7 makes seeing 42² = 49 = -1 easier

HagenvonEitzen

I'm obsessed with your channel and videos, plz upload more of em including some "floor" function related videos, that would be great !

chhabisarkar

FALL IN LOVE WITH UR CHANNEL!! thank for your material which is really helpful for everyone!!! HOPE YOU WILL BE 4EVA here) wish u success !

excited

Found it easier to do Mod(5) both side . it will concluded that n can be only 1, 6, 11, 16, 21 or n=5x+1 form. put it back in equation will get 5^l * 43^m = (5x) * (25x^2 + 15x + 3) . because the primeness .5^l = 5x and 43^m = 25x^2 + 15x + 3

bosorot

Can you kindly explain the line where you took the set of {1, 43, -1, -43}mod(25)? What is the process there? Thanks 😊

ceooflslam

One small correction this is problem 3 not 4, i think.

exarchoustathees

Hi Letsthinkcritically, I am back with my half baked solution :) Can you please guide me as to how move forward with this approach to provide a well rounded solution? By inspection we notice that the parity of n is even. This means n^3-1 divides 215.(this is because l and m are naturals, so the min value of LHS is 215). We notice that n = 6 holds for l=1, m=1. How do I proceed from here and consider other cases and prove that this is the only solution? (using the parity approach)? Please guide

karthikkrishnaswami

Are there specifications somewhere for the IMO that state 0 is not in N? Or if you asked a proctor, would they be able to tell you? Most of the time I myself and classes I’ve been in have taken 0 to be a member of N, so I was wondering where the IMO people clarify that.

Deathranger

Wo else thought it was 5^l * 4 * 3^m + 1 = n^3?

cr

i am always disappointed when a glaringly obvious solution turns out to be the *only* solution.

piman

I dont inderstand why de have contradiction in the end of this vidéo

mohamedhachi

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