How to prove a GCD question?
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
19164
On the GCD of a Pair of Fermat Numbers
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
82777
If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$?
20477
Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$
93930
GCD of the already GCD
67660
Prove $\,b\equiv c\pmod{\!m}\Rightarrow \gcd(b,m)=\gcd(c,m)$ i.e. $\gcd(c+km,m) = \gcd(c,m)$
107095
Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
19500
How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
95889
Prove that $\gcd(n! + 1, 3n! + 1) = 1$, $\forall n \in \mathbb{N}$, $n \geq 2$.
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
57281
Is Bezout's lemma enough to confirm the GCD of a number.
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$