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 10 October 2016.
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