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integer polynomial

Source: VI - Rioplatense 1997 L3 P1

September 19, 2022
polynomialalgebra

Problem Statement

Find all positive integers nn with the following property: there exists a polynomial Pn(x)P_n(x) of degree nn, with integer coefficients, such that Pn(0)=0P_n(0)=0 and Pn(x)=nP_n(x)=n for nn distinct integer solutions.
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