BdMO Online Forum

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 $n$.