Can $n!+4$ be a perfect square when $n\geq5$? I tried to check if there is any perfect squares that is form of $n!+4$, but I didn't succeed.
I think $n!+4$ can be a perfect square when $n\geq5$, since $n!+4$ when $n>5$ is $0 \pmod {4}$ and $1 \pmod {3}$.