Brocard problem

The Brocard problem is the problem of finding the integer solutions of the equation


    n! + 1 = m 2


These solutions are called Brown numbers, and only three of them are known: (5, 4), (11, 5), and (71, 7). Paul Erdös conjectured that there are no others.


The problem was posed by Henri Brocard (1845–1921) in a pair of articles in 1876 and 1885, and independently in 1913 by Srinivasa Ramanujan.