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Q(y) R(y)= P(5y^2) when P(x) = x^4 + x^3 + x^2 + x + 1

Source: Austrian - Polish 1995 APMC

May 3, 2020
polynomialalgebraInteger Polynomial

Problem Statement

Let P(x)=x4+x3+x2+x+1P(x) = x^4 + x^3 + x^2 + x + 1. Show that there exist two non-constant polynomials Q(y)Q(y) and R(y)R(y) with integer coefficients such that for all Q(y)ā‹…R(y)=P(5y2)Q(y) \cdot R(y)= P(5y^2) for all yy .
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