Showing that gcd(a,b) = gcd(c,d) in this case
25825
Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
23590
Show that $\gcd\left(\frac{a^n-b^n}{a-b},a-b\right)=\gcd(n d^{n-1},a-b)$
72424
Suppose 1 ≤ k ≤ n − 1 and gcd(k, n) = 1. Prove that gcd(n − k, n) = 1
125737
GCD( LCM(a,b) , LCM(a,c) ) = LCM(b, GCD(b,c)) , why?
11600
$\gcd(a,\operatorname{lcm}(b,c))=\operatorname{lcm}(\gcd(a,b),\gcd(a,c))$
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
74924
identity element of $(D_n ,\gcd)$
117098
Properties of the greatest common divisor: $\gcd(a, b) = \gcd(a, b-a)$ and $\gcd(a, b) = \gcd(a, b \text{ mod } a)$
121156
Prove that: $\gcd[a,b,c]=\frac{abc.\operatorname{lcm}(a,b,c)}{\operatorname{lcm}(a,b)\operatorname{lcm}(a,c)\operatorname{lcm}(b,c)}$
65687
$\gcd(a,b)\gcd(x,y)\mid ax+by$
151434
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$