A Proof of Wilson’s Theorem (Without Using Modular Arithmetic)

Question

Wilson’s Theorem says that any number $n$ is a prime number if, and only if, $(n−1)!+1$ is divisible by $n$. I came across this theorem and a proof for it in some obscure math textbook that I borrowed from a friend. The thing is, school’s closed for the summer and I have no way of getting that book from him anytime soon. I remember the proof being really easy to follow, and it made no use of modular arithmetic at all. Naturally, I’ve forgotten the proof and I can’t seem to find it anywhere. I can’t seem to prove it myself either. Anyway, the only observation I’ve made so far is that $\frac{(n-1)!+1}{n}$ can equivalently be written as $[(1-\frac{1}{n})(n-2)!]+\frac{1}{n}$. I’m not even sure if this is of any help, but it’s as far as I’ve gotten. I’m beginning to think that the proof I’m looking for doesn’t even exist. I’d appreciate it if someone pointed me in the right direction, or gave the entire proof.