Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
39563
How to show $a,b$ coprime to $n\Rightarrow ab$ coprime to $n$?
158308
Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
11600
$\gcd(a,\operatorname{lcm}(b,c))=\operatorname{lcm}(\gcd(a,b),\gcd(a,c))$
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
72747
Proving gcd($a,b$)lcm($a,b$) = $|ab|$
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?
56612
Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]
60842
if $a^2+b^2=c^2$ then $gcd(a,b)=gcd(a,c)=gcd(b,c)$.
72424
Suppose 1 ≤ k ≤ n − 1 and gcd(k, n) = 1. Prove that gcd(n − k, n) = 1
22845
Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
82777
If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$?
151434
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
81794
Prove that $(ab,cd)=(a,c)(b,d)\left(\frac{a}{(a,c)},\frac{d}{(b,d)}\right)\left(\frac{c}{(a,c)},\frac{b}{(b,d)}\right)$