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Polynomial Identity

Source: 2022 IZHO P1, https://izho.kz/contest/problems/

February 18, 2022
algebrapolynomial

Problem Statement

Non-zero polynomials P(x)P(x), Q(x)Q(x), and R(x)R(x) with real coefficients satisfy the identities P(x)+Q(x)+R(x)=P(Q(x))+Q(R(x))+R(P(x))=0. P(x) + Q(x) + R(x) = P(Q(x)) + Q(R(x)) + R(P(x)) = 0. Prove that the degrees of the three polynomials are all even.
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