Brocard’s problem

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. Erdős believed that there are no other solutions, and no more have been found for $n$ up to ${10}^9$.

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