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P(x)^2 +P(-x) = P(x^2)+P(x) , polynomial

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 2001 p1

February 11, 2020
functional equationfunctionalpolynomialalgebra

Problem Statement

Determine all polynomials PP such that for every real number xx, P(x)2+P(āˆ’x)=P(x2)+P(x)P(x)^2 +P(-x) = P(x^2)+P(x)
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