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Benelux Olympiad 2020, Problem 1 (polynomials attaining unit values)

Source: BxMO 2020, Problem 1

May 2, 2020
algebraBxMOBenelux

Problem Statement

Find all positive integers dd with the following property: there exists a polynomial PP of degree dd with integer coefficients such that ∣P(m)∣=1\left|P(m)\right|=1 for at least d+1d+1 different integers mm.
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