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monic integer polynomials Q(0) = 0 and P(Q(x)) = (x-1)(x-2)...(x-15).

Source: Romania IMO TST 1989 1.2

February 17, 2020
Integer Polynomialpolynomialalgebra

Problem Statement

Find all monic polynomials P(x),Q(x)P(x),Q(x) with integer coefficients such that Q(0)=0Q(0) =0 and P(Q(x))=(x−1)(x−2)...(x−15)P(Q(x)) = (x-1)(x-2)...(x-15).
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