Consider $4!=24$, if you add one you get $25=5^2$. The same occurs with $5! = 120 = 11^2 - 1$, and $7! = 5040 = 71^2 - 1$. Are there other solutions of the equation $n!+1 = m^2$?

I verified that no other solution exists with $m<10^9$. Does the problem has already been studied? Is there a demonstration that no other solution exists?

Greetings.