If $a, b, c$ are integers, $\gcd(a,b) = 1$ then $\gcd (a,bc)=\gcd(a,c)$
39563
How to show $a,b$ coprime to $n\Rightarrow ab$ coprime to $n$?
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?
74631
For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
60842
if $a^2+b^2=c^2$ then $gcd(a,b)=gcd(a,c)=gcd(b,c)$.
78031
$c\mid a,b\iff c\mid\gcd(a,b)$ [GCD Universal Property]
107914
Expanding GCDs Reasoning: $\gcd(a,c) \cdot \gcd(b,c) = \gcd(ab,bc,ac,cc)$
90480
Code for (a,b) with gcd(a,b)=1?
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
32344
Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
1991
If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$
118809
If $a$ divides $bc$ and $\gcd(a,b) = d$ then $\frac a d$ divides c
5789
$ d = \gcd(a,b)\Rightarrow\ \gcd(a/d,b/d) = 1$