2019 OIM Problems/Problem 6

Problem

Let $a_1, a_2, \cdots , a_{2019}$ be positive integers and $P$ be a polynomial with integer coefficients such that, for every positive integer $n$,

\[P(n)\;|\;a_1^n+a_2^n+\cdots + a_{2019}^n\]

Prove that $P$ is a constant polynomial.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

OIM Problems and Solutions