If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
190
Why $\gcd(qb+r,b)=\gcd(b,r)$?
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
422
If $\gcd(a,b)=1$, $\gcd(a,y)=1$ and $\gcd(b,x)=1$ then prove that $ax+by$ is prime to $ab$
145354
What is $\gcd(0,0)$?
82938
$\gcd(a,b)=1, x^a = y^b\Rightarrow x = n^b$, $ y = n^a$ for an integer $n$.
72747
Proving gcd($a,b$)lcm($a,b$) = $|ab|$
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
22845
Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
44076
Proving if $d_0$ is the smallest positive integer in $S$ then $d_0 = \gcd(a,b)$
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
7090
Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$