let $a,b$, and $c$ be integers with $b \ne 0$, and $b|c$. Prove that $\gcd(a,b) =\gcd(a+c, b)$
190
Why $\gcd(qb+r,b)=\gcd(b,r)$?
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
72424
Suppose 1 ≤ k ≤ n − 1 and gcd(k, n) = 1. Prove that gcd(n − k, n) = 1
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
107095
Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
422
If $\gcd(a,b)=1$, $\gcd(a,y)=1$ and $\gcd(b,x)=1$ then prove that $ax+by$ is prime to $ab$
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
127993
Let $p$ be a prime. Suppose that $\gcd(a, b) = p$. Find $\gcd(a^2,b)$ for all integers $a$ and $b$.
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 $
1991
If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
19656
Proving that $ \gcd(a,b) = as + bt $, i.e., $ \gcd $ is a linear combination.