greater divior polynomials

Question

Let $n,m$ be positive integers and $d = \gcd(n,m). $

Prove that $\gcd(x^{n} -1 ,x^{m} -1) = x^{d} -1$.

Is this correct?

Bezout : integers $r,s$: $\quad r(x^{n} -1) + s(x^{m} -1) = rx^{n} +sx^{m} - (r+s) = x^{d} -1$