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Omni-MATH / 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…

Problem

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problem

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 $\deg{P}=m$ and $\deg{Q}=n$,satisfy that $$P(Q(t))\not=Q(P(t))$$ holds for any real number tt.
Plain-text mathematical notation (without MathML)
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.
Original LaTeX notation
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 $t$.

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Source and history

task_id
b746bf43-e512-5477-8aaf-46231dbd4ba2
task_key
test--b746bf43-e512-5477-8aaf-46231dbd4ba2
task_revision_id
1
config / split
/ test

Official source

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