If d=gcd(a,b). Prove that a/d and b/d are relatively prime.
22845
Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
149993
Use the Euclidean algorithm to prove that gcd(na, nb) = n gcd(a, b).
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
27250
Greatest common divisor of two relatively primes
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
74631
For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
7090
Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$
1991
If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$