Problem 976

Erdős Problem #976: declared status 'open'. Formalized: no. Let $f\in \mathbb{Z}[x]$ be an irreducible polynomial of degree $d\geq 2$. Let $F_f(n)$ be maximal such that there exists $1\leq m\leq n$ with $f(m)$ is divisible by a prime $\geq F_f(n)$. Equivalently, $F_f(n)$ is the greatest prime divisor of$$\prod_{1\leq m\leq n}f(m).$$Estimate $F_f(n)$. In particular, is it true that $F_f(n)\gg n^{1+c}$ for some constant $c>0$? Or even $\gg n^d$? Prize: no. Tags: number theory.