Brocard’s problem

Brocard’s problem, first posed by Henri Brocard in 1876, asks for factorialsMathworldPlanetmath that are one less than a square, that is, solutions to the equation n!+1=m2. Only three solutions are known: 4!+1=52, 5!+1=112 and 7!+1=712. Srinivasa Ramanujan also pondered the problem, in 1913. Erdős believed that there are no other solutions, and no more have been found for n up to 109.


  • 1 P. Erdős, & R. Obláth, “Über diophantische Gleichungen der Form n!=xp±yp und n!±m!=xpActa Szeged. 8 (1937): 241 - 255
Title Brocard’s problem
Canonical name BrocardsProblem
Date of creation 2013-03-22 18:09:59
Last modified on 2013-03-22 18:09:59
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 4
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A25