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 $\gcd(a,b)=1$.
$gcd\left(2^{2^n}+1, 2^{2^m}+1\right)$
0
$\begingroup$
number-theory
greatest-common-divisor
fermat-numbers
-
0Why in the world was this question closed?? – 2017-01-10
-
0A, I didn't see the duplicate. – 2017-01-10