modular arithmetic - GCD of two polynomials in Mod 2

Let $p$ and $q$ be distinct primes.

I wonder is the following statement always true?
$$\gcd(x^p-1, x^q-1) \stackrel{?}{=} x-1$$

Answer

More generally, we have $\gcd(x^n-1,x^m-1)=x^{\gcd(n,m)}-1$.