$gcd(i,n)=1 \iff n\nmid ik$ for all $1 \leq k \leq n-1$
117468
$o(g^{k})=\frac{o(g)}{\gcd(o(g),k)}$ order of a power of a group element.
5789
$ d = \gcd(a,b)\Rightarrow\ \gcd(a/d,b/d) = 1$
59566
Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
74924
identity element of $(D_n ,\gcd)$
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
14210
Fibonacci divisibilty properties $ F_n\mid F_{kn},\,$ $\, \gcd(F_n,F_m) = F_{\gcd(n,m)}$
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
112031
Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
156966
Prove that if $b = dk$ where $gcd(m, a) = d$, there are $d$ solutions to $ax \equiv b \mod m$
32344
Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.
154959
Proof of associativity of GCD?
20574
Understanding the proof for $\gcd (F_n, F_{n+k}) = 1$ where $F_n$ is a Fermat number
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
81864
Finite group of order $mn$ with $\gcd(m,n) = 1$ .
7151
Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$.
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.