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 . Only three solutions are known: , and . Srinivasa Ramanujan also pondered the problem, in 1913. Erdős believed that there are no other solutions, and no more have been found for up to .
- 1 P. Erdős, & R. OblÃÂ¡th, “Über diophantische Gleichungen der Form und ” Acta Szeged. 8 (1937): 241 - 255