What is the identity element of the operation $x*y=\gcd(x,y)$?
74924
identity element of $(D_n ,\gcd)$
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
105975
Given the OneIdentity attribute why is GCD[a] evaluated to GCD[a]?
154959
Proof of associativity of GCD?
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
135086
GCD of two numbers divided by their greatest common divisor is 1
38547
Why does the Euclidean algorithm for finding GCD work?
5789
$ d = \gcd(a,b)\Rightarrow\ \gcd(a/d,b/d) = 1$
51538
Intuition for $\,c\mid a,b \iff c\mid \gcd(a,b)$
25825
Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$
117098
Properties of the greatest common divisor: $\gcd(a, b) = \gcd(a, b-a)$ and $\gcd(a, b) = \gcd(a, b \text{ mod } a)$
81671
Proof of identity $\sqrt {xy} = \sqrt x \sqrt y$ for $x,y \in \mathbb R^+$
14658
Deriving Chinese Remainder Theorem from gcd Bezout identity
11600
$\gcd(a,\operatorname{lcm}(b,c))=\operatorname{lcm}(\gcd(a,b),\gcd(a,c))$
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
44100
Prove that identity element is unique