Prove that $gcd(\mid G:H\mid,\mid G:K\mid )=1\Rightarrow G=HK$
102979
If $[G:H]$ and $[G:K]$ are relatively prime, then $G=HK$
7967
Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
90283
Proof that $3 \mid \left( a^2+b^2 \right)$ iff $3 \mid \gcd \left( a,b\right)$
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
78852
If $\gcd(m,n) =1, $ then $m\mathbb{Z}/ mn\mathbb{Z} \cong \mathbb{Z}/(n)$
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
116175
Show that $\gcd(3k+2,5k+3)=1$
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
65687
$\gcd(a,b)\gcd(x,y)\mid ax+by$
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
56878
Proof that $a\mid b \land b\mid c \Rightarrow a\mid c $
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$