# Math Help - Proof of integers

1. ## Proof of integers

Let a,b and n be positive integers with n ≥ 2. Prove that:

gcd((n^a) - 1, (n^b) - 1)= n^(gcd(a,b)) - 1.

Help please!! I have no idea how to do this!

2. A starting point might be similar to:
$
x^6-1 = (x^2-1)(x^4+x^2+1)
$

so if n = dk, with d = gcd(n,m)
$
x^n-1 = (x^d-1)(x^{d*(k-1)}+...)
$

and the same for m = dq
$
x^m-1 = (x^d-1)(x^{d*(q-1)}+...)
$