Why if $Z/m\oplus Z/n = Z/mn$ then $(n,m)=1$
5223
$\mathbb{Z}_m \times \mathbb Z_n$ is cyclic if and only if $\gcd(m,n)=1$
95379
Prove that $V = V_1 \oplus V_2$ in the following
127978
Another point of view that $\mathbb{Z}/m\mathbb{Z} \times\mathbb{Z}/n\mathbb{Z}$ is cyclic.
49294
prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$
103572
Does $\sum_{m=1}^{\infty}\sum_{n=1}^{\infty}a_{mn}^3=\sum_{n=1}^{\infty}\sum_{m=1}^{\infty}a_{mn}^3$ occur here?
41779
Is $x/x$ equal to $1$
148906
Finding integers $m,n$ such that $(m-n)^2=4mn/(m+n-1)$
53364
dim$(V)$ = $n$, dim$(W)$ = $m$ $\implies$ dim($L(V,W)$) = $nm$
109745
If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
81864
Finite group of order $mn$ with $\gcd(m,n) = 1$ .
15000
Show that number of elements in $(Z/nZ)^*$ is $\phi (n)$
76527
If $x_{m+n} \le x_n+x_m$, then $\lim x_n/n$ exists and is equal to $\inf x_n/n$
72640
$(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$
93031
How to show that $\mathbb{Z}$ with the operation $m*n=m+(-1)^m n$ is associative?
25004
Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically
30752
Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$