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Claim. Alexandru Pascadi, Large sieve inequalities for exceptional Maass forms and the greatest prime factor of $n^2+1$, Forum of Mathematics, Pi 14 (2026), e8. Theorem 1.1 states that $P^+(m^2+1)>m^{1.3}$ for infinitely many $m$. Its proof (Section 6.3, Notation 6.7 and (6.20), with the concluding estimates on pp. 51--52) asserts the stronger dyadic bound

$$P^+\!\left(\prod_{x\leq m\leq2x}(m^2+1)\right)\geq x^{1.30008}$$

for every sufficiently large real $x$. With $x=n/2$ the dyadic product divides $\prod_{m\le n}(m^2+1)$, so $F_{t^2+1}(n)\geq2^{-1.30008}n^{1.30008}$ for all large $n$, in the notation of Problem 976. The assertion and this consequence are recorded on the dyadic bound card.

Covers. The first question for $f(t)=t^2+1$. It does not give $F_{t^2+1}(n)\gg n^2$ and covers no other polynomial.

Depends on. No page of this wiki.

Acceptance. Refereed: published in Forum of Mathematics, Pi 14 (2026), e8, online 24 February 2026. The dyadic bound is an assertion inside the published proof, not the wording of Theorem 1.1. The site labels the problem OPEN.