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Brocard's problem, first posed by Henri Brocard in 1876, asks for factorials that are one less than a square, that is, solutions to the equation $n! + 1 = m^2$ . Only three solutions are known: $4! + 1 = 5^2$ , $5! + 1 = 11^2$ and $7! + 1 = 71^2$ . Srinivasa Ramanujan also pondered the problem, in 1913. Erdos believed that there are no other solutions, and no more have been found for
$n$ up to $10^9$ .
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- P. Erdos, & R. Obláth, ``Über diophantische Gleichungen der Form $n! = x^p \pm y^p$ und $n! \pm m! = x^p$ '' Acta Szeged. 8 (1937): 241 - 255
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