Why gcd(a,b) is the same as solving for gcd(b,a-b) in the Euclidean algorithm
117098
Properties of the greatest common divisor: $\gcd(a, b) = \gcd(a, b-a)$ and $\gcd(a, b) = \gcd(a, b \text{ mod } a)$
23048
The ring $\mathbb Z[\sqrt{-2}]= \{a+b\sqrt{-2} ; a\in \mathbb Z,b\in \mathbb Z \}$ has a Euclidean algorithm
60842
if $a^2+b^2=c^2$ then $gcd(a,b)=gcd(a,c)=gcd(b,c)$.
11600
$\gcd(a,\operatorname{lcm}(b,c))=\operatorname{lcm}(\gcd(a,b),\gcd(a,c))$
92630
How to prove $\gcd(a^m,b^m) = \gcd(a,b)^m$ using Bézout's Lemma
107914
Expanding GCDs Reasoning: $\gcd(a,c) \cdot \gcd(b,c) = \gcd(ab,bc,ac,cc)$
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
60596
Euclidean Algorithm for GCD of polynomials
4486
If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$
56612
Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]
38295
If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$