# Prove that if \$n + 1 | n! + 1\$ then \$n+1\$ is a prime number

How can we prove that if : $$n+1|n!+1$$ then $$n$$ is a prime number.
My try:
I try to do contrapositive: If $$n$$ is composite then $$n+1 nmid n!+1$$ and then to get that if $$n$$ is composite so $$n+1=ab$$ when $$2 le a le n$$ so that $$a|n+1$$ but here I don’t have idea how to continue, is this the good way?