Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
20477
Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$
80148
Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$
130653
$p^2$ divides $ab$ and $\gcd(a,b)=1$. Show $p^2$ divides $a$ or $p^2$ divides $b$
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
157508
prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
110313
Prove that $\gcd(f(x),g(x)) = 1$.
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
122096
Find $GCD(n^2+1,n+1)$
117098
Properties of the greatest common divisor: $\gcd(a, b) = \gcd(a, b-a)$ and $\gcd(a, b) = \gcd(a, b \text{ mod } a)$