How to prove that $\gcd(t^n-1,t^m-1)=t^{\gcd(n,m)}-1 $

Question

Possible Duplicate:
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$

Let $t$ be an element in any domain where gcd's exist. Then if $m,n$ are positive integer,prove that: $\gcd(t^n-1,t^m-1)=t^{\gcd(n,m)}-1 $