Erdős Problem 976

### What is the conjecture

https://www.erdosproblems.com/976

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 $\gg n^d$?

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Start by reviewing existing formalized conjectures in the formal-conjectures repository and compare their structure with the statement at https://www.erdosproblems.com/976. Determine the appropriate representation for this conjecture and verify that the resulting formal statement matches the stated definitions and open status.

Written by the indexing model from the issue text.