, Volume 4, Issue 1, pp 41-42

On the Brocard–Ramanujan Diophantine Equation n! + 1 = m2

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Abstract

In 1876, H. Brocard posed the problem of finding all integral solutions to n! + 1 = m2. In 1913, unaware of Brocard's query, S. Ramanujan gave the problem in the form, “The number 1 + n! is a perfect square for the values 4, 5, 7 of n. Find other values.” We report on calculations up to n = 109 and briefly discuss a related problem.