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MathNet 2020 — Math Olympiad Vault — Part 03 Question 95

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 03

Question 95

Determine all non-constant polynomials $P(x)$ and $Q(x)$ with real coefficients satisfying the equation
$$
P((Q(x))^3) = xP(x)(Q(x))^3.
$$