Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
 Already signed up? New to KöMaL?

# Problem A. 675. (September 2016)

A. 675. Let $\displaystyle r(x)$ be a polynomial with real coefficients whose degree $\displaystyle n$ is odd. Prove that the number of pairs of polynomials $\displaystyle p(x)$ and $\displaystyle q(x)$ with real coefficients satisfying the equation $\displaystyle \big(p(x)\big)^3 + q(x^2) = r(x)$, is smaller than $\displaystyle 2^n$.

Based on the problem of the 1st International Olympiad of Metropolises

(5 pont)

Deadline expired on October 10, 2016.

### Statistics:

 7 students sent a solution. 5 points: Tóth Viktor, Váli Benedek, Williams Kada. 4 points: Baran Zsuzsanna, Bukva Balázs, Kővári Péter Viktor, Matolcsi Dávid.

Problems in Mathematics of KöMaL, September 2016