Number theory - primes

Homework Statement

Let n and k be integers with n>=2 and k>=2. Prove that (n-1)|(n^k - 1).
Hence prove that if n^k - 1 is prime then n=2 and k is prime.

The Attempt at a Solution

I think you go about this question by using proof by induction. However im really not sure how to do this. Any help would be great! Thanks

Hint: $$(n-1)(n^{k-1}+n^{k-2}+\ldots+n+1)=n^k-1$$