Prove that if $a,m,n \in \mathbb{Z}^+$ and $m \ne n$ then $\gcd(a^{2^m}+1,a^{2^n}+1)$ is 1 if a is even and 2 if a is odd.
34059
$(a^{2^n}+1,a^{2^m}+1)=1 or 2$
27544
With $a,\ b,\ m,\ n\in \mathbb{Z}$. Show that if ${\rm gcd}(m,n)=1$, then ${\rm gcd}(ma+nb,mn)={\rm gcd}(a,n){\rm gcd}(b,m)$
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
158308
Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
74631
For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $
51858
Showing $\gcd(2^m-1,2^n+1)=1$
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
1197
Finding $\gcd(2n-1,2n+1)$ . . . I think it's 1 but is my logic right?
6453
Let $n \geq 1$ be an odd integer. Show that $D_{2n}\cong \mathbb{Z}_2 \times D_n$.
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.