MathNet 2015-part-02 — 191 problems (EN–VI) Question 159

Determine all polynomials $P$ with coefficients in $\mathbb{Z}$ such that, for every prime $p$ and all $u$ and $v$ in $\mathbb{Z}$ such that $p \mid u v-1$, we have $p \mid P(u) P(v)-1$.