$(a,b)=1$ $\iff~\Bbb Z_a\times\Bbb Z_b$ is cyclic
57887
When are the product of cyclic groups also cyclic?
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
120642
Let $g : \Bbb N \times \Bbb N \to\Bbb N \times \Bbb N$ defined as $g(m,n) = (m + n,m - n)$
69046
Proof of $\mathbb{Q}$ is not cyclic
4156
What is $\Bbb R^{\times}$? [unit group, ring to "times" power]
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
127720
Prove that $\bigcup_{n \in \Bbb{N}} [1/n,1] = (0,1]$.
13026
Prove that if AB=I_m, then rk(A)=rk(B).
86362
Cyclic vectors in a real vector space
77902
If $A,B,$ and $C$ are sets, then $A\times(B-C)$ = $(A \times B)$ $-$ $(A \times C)$.
158355
If $A$ commutes with $B$ and $B$ commutes with $C$, then $A$ commutes with $C$
116866
$A\times B$ connected component implies $A,B$ connect components
66313
$\mathbb{Z}[i]/(a+bi) \cong \mathbb{Z}_{a^2+b^2}$ if $(a,b)=1$
104460
When a group is cyclic
150166
What is $P([a_1,b_1]\times [a_2,b_2]\times...\times[a_k,b_k])$
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.