Prove that $\gcd(a, b) = \gcd(b, a-b)$
190
Why $\gcd(qb+r,b)=\gcd(b,r)$?
121156
Prove that: $\gcd[a,b,c]=\frac{abc.\operatorname{lcm}(a,b,c)}{\operatorname{lcm}(a,b)\operatorname{lcm}(a,c)\operatorname{lcm}(b,c)}$
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
22845
Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
158025
Intuition of why $\gcd(a,b) = \gcd(b, a \pmod b)$?
107914
Expanding GCDs Reasoning: $\gcd(a,c) \cdot \gcd(b,c) = \gcd(ab,bc,ac,cc)$
65687
$\gcd(a,b)\gcd(x,y)\mid ax+by$
95889
Prove that $\gcd(n! + 1, 3n! + 1) = 1$, $\forall n \in \mathbb{N}$, $n \geq 2$.
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
15168
If $a,b$ are positive integers such that $\gcd(a,b)=1$, then show that $\gcd(a+b, a-b)=1$ or $2$. and $\gcd(a^2+b^2, a^2-b^2)=1$ or $2 $
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
158308
Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$