## APMO 2021 P2 - Determine all such polynomials

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### APMO 2021 P2 - Determine all such polynomials

For a polynomial $P$ and a positive integer $n$, define $P_n$ as the number of positive integer pairs $(a, b)$ such that $a < b \leq n$ and $\vert P(a)\vert-\vert P(b)\vert$ is divisible by $n$. Determine all polynomial $P$ with integer coefficients such that $P_n \leq 2021$ for all positive integers $n$.
"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
John von Neumann