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q (x^2 - 2x ) = q(x-2 )^2

Source: 1974 Swedish Mathematical Competition p4

March 26, 2021
polynomialalgebra

Problem Statement

Find all polynomials p(x)p(x) such that p(x2)=p(x)2p(x^2) = p(x)^2 for all xx. Hence find all polynomials q(x)q(x) such that q(x2−2x)=q(x−2)2 q\left(x^2 - 2x\right) = q\left(x-2\right)^2
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