Problem

Source: 2023 RMM, Problem 5

Tags: Polynomials, RMM 2023, number theory, algebra



Let $P,Q,R,S$ be non constant polynomials with real coefficients, such that $P(Q(x))=R(S(x)) $ and the degree of $P$ is multiple of the degree of $R. $ Prove that there exists a polynomial $T$ with real coefficients such that $$\displaystyle P(x)=R(T(x))$$