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Polynomial stable under product

Source: Saint Petersburg 2016

December 11, 2016
algebrapolynomial

Problem Statement

A polynomial PP with real coefficients is called great, if for some integer a>1a>1 and for all integers xx, there exists an integer zz such that aP(x)=P(z)aP(x)=P(z). Find all great polynomials.
Proposed by A. Golovanov
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