$\gcd=1$ if $ m^n=ab \Rightarrow m^n=(a'b')^n$?
54554
If a product of relatively prime integers is an $n$th power, then each is an $n$th power
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
59533
If $\gcd(m,n)=1$, then $\mathbb{Z}_n \times \mathbb{Z}_m$ is cyclic.
158308
Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
83938
If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian
74924
identity element of $(D_n ,\gcd)$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
78852
If $\gcd(m,n) =1, $ then $m\mathbb{Z}/ mn\mathbb{Z} \cong \mathbb{Z}/(n)$
126280
In a P.I.D., if $a^m = b^m$ and $a^n = b^n$ for $m, n \in \mathbb{N}$ with $\gcd(m,n) = 1$, then $a=b$
63758
$c\mid ab\Rightarrow c\mid \gcd(a,c)\gcd(b,c),\,$ for integers $a, b, c$
4486
If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
55441
Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]