Problem

Source: Peru IMO TST 2016 p16

Tags: polynomial, Divisibility, divisible, algebra, positive integers



Find all pairs $ (m, n)$ of positive integers that have the following property: For every polynomial $P (x)$ of real coefficients and degree $m$, there exists a polynomial $Q (x)$ of real coefficients and degree $n$ such that $Q (P (x))$ is divisible by $Q (x)$.