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P(Q(x)) = (x - 1)(x - 2)...(x - 9), integer polynomials

Source: 2016 Saudi Arabia IMO TST , level 4, III p2

July 29, 2020
algebraInteger Polynomialpolynomial

Problem Statement

Find all pairs of polynomials P(x),Q(x)P(x),Q(x) with integer coefficients such that P(Q(x))=(x−1)(x−2)...(x−9)P(Q(x)) = (x - 1)(x - 2)...(x - 9) for all real numbers xx
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