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Claim. N. A. Carella, Largest Prime Factors of Polynomials (arXiv:2308.10075), claims in its abstract that the largest prime factor $p$ of $\prod_{x\le n\le2x}(n^2+1)$ satisfies $p\ge x^{3/2}$ as $x\to\infty$. With $x=n/2$ this would give $F_{t^2+1}(n)\gg n^{3/2}$ in the notation of Problem 976, an exponent above every published one.

Covers. The first question for $f(t)=t^2+1$. It does not claim $F_{t^2+1}(n)\gg n^2$.

Depends on. No page of this wiki.

Standing. An unrefereed arXiv note, first posted on 19 August 2023, with seven versions, the latest of 13 June 2025. No journal publication or outside review is recorded. The site labels the problem OPEN.