Math Olympiad Question｜Learn This Trick! 

Interesting thing, we can prove that it's a Fibonacci (Fn) patern ! Let's note Phi = (1+-sqrt(5))/2 then : Phi^n = Fn*Phi + Fn-1

It is possible to solve this problem in a much more efficient way then is done in the video. Evidently m and n are the roots of the quadratic equation x² = x + 1 This is a special equation with roots φ (the golden ratio) and ψ = −1/φ. For both roots of this equation we have xⁿ = Fₙx + Fₙ₋₁ where Fₙ is the n-th Fibonacci number. This can easily be proved by induction. Note that the sum of the roots of the quadratic equation is m + n = 1, so we have m⁵ + n⁵ = (F₅m + F₄) + (F₅n + F₄) = F₅(m + n) + 2·F₄ = 5·1 + 2·3 = 11.

merci, très intéressant !

So Good, trick!

Bro just complicated his life. It's way easier to solve than that.

(m+2m-5) (n+2n-5)

(m+1m-1) (n+1n-1)

I am confused as to how you know what the roots of x^2-x-1=0 at 4:20