Brocard's conjecture

Brocard's conjecture is a hypothesis in number theory proposed by the mathematician Henri Brocard in 1876. It suggests that there are only a finite number of natural numbers \( n \) such that the expression \( n! + 1 \) (the factorial of \( n \) plus one) is a perfect square. In mathematical terms, Brocard's conjecture can be stated as: There are only finitely many integers \( n \) such that: \[ n!