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International Olympiad of metropolises 2016 P5

Source: International Olympiad of metropolises 2016

September 7, 2016
IOMalgebra

Problem Statement

Let r(x)r(x) be a polynomial of odd degree with real coefficients. Prove that there exist only finitely many (or none at all) pairs of polynomials p(x)p(x) and q(x)q(x) with real coefficients satisfying the equation (p(x))3+q(x2)=r(x)(p(x))^3 + q(x^2) = r(x).
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