$P$ and $Q$ are two different non-constant polynomials such that $P(Q(x)) = P(x)Q(x)$ and $P(1) = P(-1) = 2019$. What are the last four digits of $Q(P(-1))$?
Problem
Source: 2019 Dürer Math Competition Finals Day2 E+12 https://artofproblemsolving.com/community/c1621835_2019_
Tags: number theory, polynomial, last digits, Digits