{"schema":"vela.problem-packet.v0.1","problem":976,"statement":"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","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}