I came across these theorems, I was wondering if anyone could help with them!

1. Let a, b, n be elements of N with n >= 1. Prove that a and b are relatively prime iff a^n and b are relatively prime.

2. Suppose a, b, c are elements of N with at least one not zero. How would you define the greatest common divisor of a, b, c? Prove that it exists AND is unique.

I'm pretty sure for the 2nd one that gcd(a, b, c) = gcd(gcd(a,b), c). Any help actually PROVING these?