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Polynomials P[R] such that P(x^2)=P(x)P(x+2)

Source: Czech-Polish-Slovak Match 2007-P1

September 14, 2011
algebrapolynomialcomplex numbersalgebra proposed

Problem Statement

Find all polynomials PP with real coefficients satisfying P(x2)=P(x)ā‹…P(x+2)P(x^2)=P(x)\cdot P(x+2) for all real numbers x.x.