Let a, b, c be integers with at most one of the three equal to 0. Prove that if gcd(a,c)=1, then gcd(ab,c)=gcd(b,c).
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
121156
Prove that: $\gcd[a,b,c]=\frac{abc.\operatorname{lcm}(a,b,c)}{\operatorname{lcm}(a,b)\operatorname{lcm}(a,c)\operatorname{lcm}(b,c)}$
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
7090
Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$
422
If $\gcd(a,b)=1$, $\gcd(a,y)=1$ and $\gcd(b,x)=1$ then prove that $ax+by$ is prime to $ab$
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
103147
$\operatorname{gcd}(ab,a+b)=1$ if $a$ and $b$ are relatively prime
117098
Properties of the greatest common divisor: $\gcd(a, b) = \gcd(a, b-a)$ and $\gcd(a, b) = \gcd(a, b \text{ mod } a)$
8160
What is $\gcd(0,a)$, where $a$ is a positive integer?
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
75974
$\gcd(a,b)\!=\!1\!=\!\gcd(a,c)\Rightarrow\gcd(a,bc)\!=\!1$ [coprimes to $\,a\,$ are product closed]