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integer polynomial stable under product

Source: St. Petersburg 2016 10.7

May 1, 2019
algebrapolynomialInteger PolynomialInteger

Problem Statement

A polynomial P(x)P(x) with integer coefficients and a positive integer a>1a>1, are such that for all integers xx, there exists an integer zz such that aP(x)=P(z)aP(x)=P(z). Find all such pairs of (P(x),a)(P(x),a).
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