Claims

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2015_04_25_cerda: An arXiv manuscript of 2015 presenting a method to find all solutions of n! + 1 = m^2 by modular congruences; withdrawn by its author in 2015 and again in 2016, the last time noting a mistake in the solution.

2017_02_14_sabihi: A ResearchGate manuscript claiming a short solution of n! = x^2 - 1, that n = 4, 5, 7 are the only solutions, and a generalization; rejected after a concrete error was exhibited in the site's discussion thread.

2025_08_15_naciri: Naciri proves that the only solutions of n! + 1 = x^2 with x+1 or x-1 7-free are n = 4, 5, 7, and that n = 4 is the only one with x+1 or x-1 a prime power (Integers 25 (2025), #A71).

2026_02_05_maiti: An arXiv manuscript claims, as Theorem 2.15 of its second version, that the Brocard-Ramanujan equation has no solution beyond n = 4, 5, 7, from a comparison of growth rates; unrefereed and unreviewed.

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