# Number Theory - divisibility and primes

1. Jan 22, 2009

### future_phd

1. The problem statement, all variables and given/known data
Prove that any integer n >= 2 such that n divides (n-1)! + 1 is prime.

2. Relevant equations

3. 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.

2. Jan 22, 2009

### 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).

Last edited: Jan 22, 2009