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2017 China TSTST Day 2 Polynomials

Source: 2017 China TSTST Day 2 Problem 4

March 7, 2017
TststPolynomialsalgebrapolynomialChina

Problem Statement

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