Proof that if $\gcd(a,b) = 1$ then $\gcd(a^n, b^m) = 1$
63547
Euclid's Lemma and $\gcd(a,b)=1\Rightarrow \gcd(a^n,b^k)= 1$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)
51858
Showing $\gcd(2^m-1,2^n+1)=1$
48839
Show that the order of $a\times b$ is equal to $nm$ if gcd(n,m)=1
38295
If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
92630
How to prove $\gcd(a^m,b^m) = \gcd(a,b)^m$ using Bézout's Lemma
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
80148
Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
112031
Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$