Mathematical and Physical Journal
for High Schools
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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.


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