Proving $o(g^r) = n / \gcd(n,r) $?
7843
Show that order of $a^k$
137369
Inductive proof of gcd Bezout identity (from Apostol: Math, Analysis 2ed)
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
145354
What is $\gcd(0,0)$?
73972
How to prove that $\gcd(2n^3-14n+2,n+3) = \gcd(n+3,10)$?
72424
Suppose 1 ≤ k ≤ n − 1 and gcd(k, n) = 1. Prove that gcd(n − k, n) = 1
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
139833
Prove that $\gcd(M, N)\times \mbox{lcm}(M, N) = M \times N$.
11003
Proving that $G/N$ is an abelian group
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$
158308
Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
14783
A Number Theory problem (GCD)