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P((Q(x))^3)=xP(x)(Q(x))^3 , polynomials

Source: Greek National 2020 p1 (Archimedes)

February 23, 2020
algebrapolynomialfunctional equationfunctionalpolynomial equationBelarus

Problem Statement

Find all non constant polynomials P(x),Q(x)P(x),Q(x) with real coefficients such that: P((Q(x))3)=xP(x)(Q(x))3P((Q(x))^3)=xP(x)(Q(x))^3
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