Number Theory - divisibility and primes

[future_phd]

Homework Statement

Prove that any integer n >= 2 such that n divides (n-1)! + 1 is prime.

Homework Equations

The Attempt at a Solution

I'm having trouble getting started, I have no idea how to approach this, can someone give a hint on where to begin maybe because I'm just not seeing it.

 

[wsalem]

Assuming that n divides $$(n-1) \cdot (n-2) \cdots 2 + 1$$. Show that this entails $$(n-1), (n-2), \cdots 2$$ do not divide $$n$$. In other words, nothing less than n divides n (except the trivial case).