$gcd\left(2^{2^n}+1, 2^{2^m}+1\right)$

Question

Given two Fermat's number $a=2^{2^n}+1$ and $b=2^{2^m}+1$ with $n,m\in\mathbb{Z}, ~n,m\ge0~\wedge~n\ne m$. Prove $\gcd(a,b)=1$.