Show that, if $\gcd(r,s)=1$, then $\mathbb{Z}/r \times \mathbb{Z}/s \cong \mathbb{Z}/rs$
127978
Another point of view that $\mathbb{Z}/m\mathbb{Z} \times\mathbb{Z}/n\mathbb{Z}$ is cyclic.
116175
Show that $\gcd(3k+2,5k+3)=1$
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
38295
If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
112031
Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
74631
For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $
59533
If $\gcd(m,n)=1$, then $\mathbb{Z}_n \times \mathbb{Z}_m$ is cyclic.
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
98765
Showing that $G/(H\cap K)\cong (G/H)\times (G/K)$
7151
Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$.