For all integers y, if $\gcd(9,y) = 3,$ then $\gcd(9,y^2) = 9$
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
19164
On the GCD of a Pair of Fermat Numbers
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
38295
If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
145354
What is $\gcd(0,0)$?
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$