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2019 Iberoamerican Mathematical Olympiad P6

Source:

September 16, 2019
algebrapolynomial

Problem Statement

Let a1,a2,…,a2019a_1, a_2, \dots, a_{2019} be positive integers and PP a polynomial with integer coefficients such that, for every positive integer nn, P(n) divides a1n+a2n+⋯+a2019n.P(n) \text{ divides } a_1^n+a_2^n+\dots+a_{2019}^n. Prove that PP is a constant polynomial.
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