For all $n \geq 1$, and positive integers $a,b$ show: If $\gcd (a,b)=1$, then $\gcd(a^n,b^n)=1$
92630
How to prove $\gcd(a^m,b^m) = \gcd(a,b)^m$ using Bézout's Lemma
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
18693
If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, then $a=b$
51858
Showing $\gcd(2^m-1,2^n+1)=1$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
95889
Prove that $\gcd(n! + 1, 3n! + 1) = 1$, $\forall n \in \mathbb{N}$, $n \geq 2$.
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
52357
If $a,b \in G$, show that $ab^{n}a^{-1}=(aba^{-1})^{n}$.