Show that $\gcd(ca,cb) = |c|\gcd(a,b)$
4425
Why are integer GCDs positive? [unit normalization of GCDs]
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
38295
If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
25825
Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
121156
Prove that: $\gcd[a,b,c]=\frac{abc.\operatorname{lcm}(a,b,c)}{\operatorname{lcm}(a,b)\operatorname{lcm}(a,c)\operatorname{lcm}(b,c)}$
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
11600
$\gcd(a,\operatorname{lcm}(b,c))=\operatorname{lcm}(\gcd(a,b),\gcd(a,c))$
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
4486
If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$
72424
Suppose 1 ≤ k ≤ n − 1 and gcd(k, n) = 1. Prove that gcd(n − k, n) = 1
118809
If $a$ divides $bc$ and $\gcd(a,b) = d$ then $\frac a d$ divides c
78031
$c\mid a,b\iff c\mid\gcd(a,b)$ [GCD Universal Property]
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$