If $a = r \pmod b$ when $0 \le r < b$, then $\gcd(a, b) = \gcd (b, r)$
190
Why $\gcd(qb+r,b)=\gcd(b,r)$?
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
151434
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
32344
Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
36043
If $ab \equiv r \pmod{p}$, and $x^2 \equiv a \pmod{p}$ then $y^2 \equiv b \pmod{p}$ for which condition of $r$?
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
90480
Code for (a,b) with gcd(a,b)=1?
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,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 $
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
7151
Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$.
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$