If $m \equiv m'$ mod $n$, then gcd$(m,n) = 1$ $\Longleftrightarrow$ gcd$(m',n) = 1$.
190
Why $\gcd(qb+r,b)=\gcd(b,r)$?
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
72640
$(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$
117098
Properties of the greatest common divisor: $\gcd(a, b) = \gcd(a, b-a)$ and $\gcd(a, b) = \gcd(a, b \text{ mod } a)$
22845
Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
67660
Prove $\,b\equiv c\pmod{\!m}\Rightarrow \gcd(b,m)=\gcd(c,m)$ i.e. $\gcd(c+km,m) = \gcd(c,m)$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
86413
Show that $\frac{(m+n-1)!}{m!n!}$ is an integer where m and n are positive integers and gcd(m,n)=1
119051
Show that only finitely many positive integers $n$ have the property that for all $m$ for which $1<m<n$ and $\text{gcd}(m,n) = 1$, $m$ is prime.
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
38295
If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
63769
Group theory proof of Euler's theorem ($a^{\phi(m)} \equiv 1\mbox{ }(\mbox{mod }m)$ if $\gcd(a,m)=1$)
59566
Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
37596
If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
81864
Finite group of order $mn$ with $\gcd(m,n) = 1$ .
96535
Show that if $\gcd(a,3)=1$ then $a^7 \equiv a\pmod{63}$. Why is this assumption necessary?