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Polynomials

Source: Iran 3rd round 2017 first Algebra exam

August 7, 2017
algebrapolynomialIranIranMO

Problem Statement

Find all polynomials P(x)P(x) and Q(x)Q(x) with real coefficients such that P(Q(x))=P(x)2017P(Q(x))=P(x)^{2017} for all real numbers xx.