Prove: $(n-1)! \equiv -1 \pmod{n}$ I'm trying to self-learn some number theory. Currently, I'm trying to prove the following:
$$(n-1)! \equiv -1 \pmod{n}$$
However, I'm a bit stumped on this one. Honestly, I'm not sure where's a good place to start.

This is false for general $n$.  For example, $5!=120\equiv 0\pmod 6$, not $-1$.  In fact, $(n-1)!\equiv 0\pmod{n}$ for all composite $n\geq 6$.
