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Claim. The answer to Problem 398 is yes: $n=4,5,7$ are the only solutions of $n!=x^2-1$. Ahmad Sabihi's manuscript A short solution for Brocard-Ramanujans' problem (Erdős' conjecture) and its generalization, posted on ResearchGate as publication 313677604 and linked above, claims an elementary proof of this statement and of a generalization. The manuscript was posted on ResearchGate on 14 February 2017, the upload date its file identifier encodes, and the page is dated by that posting; it was brought to the site's discussion thread on 19 October 2025 with a request for a professional reading. It was not submitted to the site's proof-claims tab, and the site's problem page does not mention it.

Standing. Rejected. Thomas Bloom, the site's curator, replied in the thread the same day that the manuscript has not appeared in a peer-reviewed journal, that its methods are elementary case analysis, and that a proof of this problem without deeper machinery is unlikely, without locating an error. On 17 November 2025 Stijn Cambie wrote of having asked the author, who had not submitted the manuscript anywhere and knew of no mistake, and then reported two errors: equation (4.28) has many solutions for the quantity $c$ where the argument needs one, so the appendix does not do what the argument asks of it; and at the top of p. 14 the step fails when the quantity $A$ is itself prime, with $n=32$, $A=17$ as an explicit example, because the inequality $p^2\le n!$ invoked there has no bearing on the divisibility in question. No reply by the author is in the thread, no refereed publication or independent review exists, and the site's label is unchanged. The claim is recorded as rejected on the error exhibited in the thread; the manuscript is not held in the library, and this record rests on the thread.

Depends on. No page of this wiki.