MathDB

1

Part of 2022 International Zhautykov Olympiad

Problems(1)

Polynomial Identity

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

2/18/2022
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.
algebrapolynomial