Prove that $\gcd(g_a,g_b) = 1$ given that for $n \in Z^{\geq 0}$, define $g_n = 2^{2^n} + 1$
25034
Fermat numbers are coprime
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
20477
Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$
19500
How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?
147802
Proving that $\gcd\left(\frac a {\gcd(a,b)},\frac b {\gcd(a,b)}\right) =1$
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
122096
Find $GCD(n^2+1,n+1)$
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
84501
Proof involving Cyclic group, generator and GCD
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$