[math-fun] Squares and factorials

There are at least three solutions to the Diophantine equation: m² = n! + 1 namely (m,n) = (5,4), (11,5), and (71,7). As far as I know, no further pairs have been discovered. Is there a proof that these three solutions are the only ones in existence, or could there be others? 71 seems to exhibit other interesting properties, being the largest prime factor of the order of the Monster Group, and the largest supersingular prime. But 24 definitely wins as the most interesting integer... Sincerely, Adam P. Goucher