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2023 RMM, Problem 5

Source: 2023 RMM, Problem 5

March 4, 2023
PolynomialsRMM 2023number theoryalgebra

Problem Statement

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