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Claim. Somnath Maiti, Results of Brocard-Ramanujan problem on diophantine equation $n!+1=m^2$ (arXiv:2004.09256), states as Theorem 2.15 of its second version (5 February 2026) that the equation has no solution beyond $n=4,5,7$, the answer yes to Problem 398. Its introduction and Conclusion 2.16 say that the study claims to establish this. It also states as Theorem 2.5 that the equation has only finitely many solutions, unconditionally. The first version (9 April 2020) claimed only the finiteness and said that the stronger statement had not been established, so the page is dated by the second version, the first posting of the full claim. The manuscript writes $\sqrt{n!}=k+\epsilon$ with $0<\epsilon<1$, notes that a solution needs $n!=k(k+2)$, and bounds from below the value of $\epsilon$ a new solution with $n\geq10^5$ would need.

Standing. Claimed. The manuscript is unrefereed, was not posted to the site, and no review of it is known. The proof of Theorem 2.15 compares the growth of $k=\lfloor\sqrt{n!}\rfloor$ with that of $\epsilon=\sqrt{n!}-k$ and asserts, without an estimate, that $\epsilon$ cannot reach the value a solution needs.

Depends on. No page of this wiki.