Prove that $d$ is a gcd of $a_1, ..., a_n$ iff $\langle d\rangle = \langle a_1\rangle + \cdots + \langle a_n\rangle$.
51974
Does the Bezout GCD equation hold in a UFD?
32735
If $ \langle G, \star \rangle $ is an abelian group, then for all $a, b \in G$, show that $(a \star b)^{n} = a^{n} \star b^{n}$.
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
128199
Proving gcd(a, a+2) is 1 or 2 for every integer a?
32108
$ a\in \Bbb Z_n$ is invertible $\,\Rightarrow\gcd (a,n) =1$
98352
If $k|n$, then $D_{2n}/\langle{r^k}\rangle\cong D_{2k}$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
78852
If $\gcd(m,n) =1, $ then $m\mathbb{Z}/ mn\mathbb{Z} \cong \mathbb{Z}/(n)$
82777
If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$?
38295
If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
95889
Prove that $\gcd(n! + 1, 3n! + 1) = 1$, $\forall n \in \mathbb{N}$, $n \geq 2$.
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?
157508
prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$