Problem

Source: 2017 China TSTST Day 2 Problem 4

Tags: Tstst, Polynomials, algebra, polynomial, China



Find out all the integer pairs $(m,n)$ such that there exist two monic polynomials $P(x)$ and $Q(x)$ ,with $\deg{P}=m$ and $\deg{Q}=n$,satisfy that $$P(Q(t))\not=Q(P(t))$$holds for any real number $t$.