Showing $\gcd(2^m-1,2^n+1)=1$
45037
Show $(2^m-1,2^n+1)=1$ if $m$ is odd
63965
How can I compute the sum of $ {m\over\gcd(m,n)}$?
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
42780
Show that if $a^{n-1} \equiv 1 \pmod{n}$ for all $a$ such that $\gcd(n,a) = 1$, then $a^{n} \equiv a \pmod{n}$ for all $a$.
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
7151
Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$.
72424
Suppose 1 ≤ k ≤ n − 1 and gcd(k, n) = 1. Prove that gcd(n − k, n) = 1
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
20477
Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
7090
Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$
14693
$d = \gcd(c,m),\ ac≡bc\pmod{\! m}\Rightarrow a≡b\pmod {\!m/d}\ $ [Congruence Cancellation & Division Rule]
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $