$n!+1$ being a perfect square One observes that 
\begin{equation*}
4!+1 =25=5^{2},~5!+1=121=11^{2} 
\end{equation*}
is a perfect square. Similarly for $n=7$ also we see that $n!+1$ is a perfect square. So one can ask the truth of this question:


*

*Is $n!+1$ a perfect square for infinitely many $n$? If yes, then how to prove.


The sequence of factorials $n!+1$ which are also perfect squares is here in Sloane. It contains three terms, and notes that there are no more terms below $(10^9)!+1$, but as far as I  know there's no proof.
