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P(x^2)=P(x)P(x-1) over R

Source: 2001 Moldova MO Grade 12 P3

April 13, 2021
functional equationfePolynomialsalgebra

Problem Statement

Find all polynomials P(x)P(x) with real coefficieints such that P(x2)=P(x)P(x−1)P\left(x^2\right)=P(x)P(x-1) for all x∈Rx\in\mathbb R.
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