MathNet 2022-part-02 — 197 problems (EN–VI) Question 49

Find all polynomials $P(x)$ with integral coefficients and the following property: for any pair $(u, v)$ of positive integers, $\text{gcd}(u, v) = 1$ implies $\text{gcd}(|P(u)|, |P(v)|) = 1$.