# Number theory - primes

1. Mar 17, 2009

### Fairy111

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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

2. Mar 17, 2009

### yyat

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

3. Mar 17, 2009

### Fairy111

its supposed to be n^(k) - 1

4. Mar 17, 2009

### yyat

Isn't that the same as the RHS of the formula I wrote?