Let $f \in Z [x]$ 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 $1 \leq m \leq n \prod f (m) .$ Estimate $F_{f} (n)$ . In particular, is it true that $F_{f} (n) ≫ n^{1 + c}$ for some constant $c > 0$ ? Or even $≫ n^{d}$ ?

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number theory · open · 0 attempts

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vela reproduce examples/erdos-problems

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gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Write (P^+(N)) for the largest prime factor of a nonzero integer (N). Then your quantity is [ F_f(n)=P^+!\Big(\prod_{m\le n}f(m)\Big)=\max_{m\le n}P^+(f(m)). ]

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llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

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