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integer P, x^m + x + 2 = P(P(x)) , for all integers x

Source: 2015 Latvia BW TST P3

December 16, 2022
polynomialInteger Polynomialalgebra

Problem Statement

Prove that there does not exist a polynomial P(x)P (x) with integer coefficients and a natural number mm such that xm+x+2=P(P(x))x^m + x + 2 = P(P(x)) holds for all integers xx.
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