Brocard's Problem

Unsolved Problem
For which pairs of (strictly) positive integers $\left({m, n}\right)$ do the following hold:
 * $n! + 1 = m^2$

The only known pairs are:
 * $(1): \quad \left({5, 4}\right): 4! + 1 = 24 + 1 = 25 = 5^2$
 * $(2): \quad \left({11, 5}\right): 5! + 1 = 120 + 1 = 121 = 11^2$
 * $(3): \quad \left({71, 7}\right): 7! + 1 = 5040 + 1 = 5041 = 71^2$

Also see

 * Definition:Brown Numbers