Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$.
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$
98946
Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
72424
Suppose 1 ≤ k ≤ n − 1 and gcd(k, n) = 1. Prove that gcd(n − k, n) = 1
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$
72640
$(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
67660
Prove $\,b\equiv c\pmod{\!m}\Rightarrow \gcd(b,m)=\gcd(c,m)$ i.e. $\gcd(c+km,m) = \gcd(c,m)$
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
81864
Finite group of order $mn$ with $\gcd(m,n) = 1$ .
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$