2019 OIM Problems/Problem 6
Problem
Let 
be positive integers and 
be a polynomial with integer coefficients such that, for every positive integer 
,
![\[P(n)\;|\;a_1^n+a_2^n+\cdots + a_{2019}^n\]](http://latex.artofproblemsolving.com/8/0/2/802ad7c3000d4a54a8c79fc42d20a54756a68d0e.png)
Prove that is a constant polynomial.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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