if the gcd of (a,b) = 1, and a,b divide an integer x, prove that ab ≤x
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
147902
Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$
5789
$ d = \gcd(a,b)\Rightarrow\ \gcd(a/d,b/d) = 1$
15168
If $a,b$ are positive integers such that $\gcd(a,b)=1$, then show that $\gcd(a+b, a-b)=1$ or $2$. and $\gcd(a^2+b^2, a^2-b^2)=1$ or $2 $
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
82938
$\gcd(a,b)=1, x^a = y^b\Rightarrow x = n^b$, $ y = n^a$ for an integer $n$.
147527
Let $a$ and $b$ be non-zero integers, and $c$ be an integer. Let $d = \gcd(a, b)$. Prove that if $a|c$ and $b|c$ then $ab|cd$.
8160
What is $\gcd(0,a)$, where $a$ is a positive integer?
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
37596
If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$