For $D$ a GCD domain , let $a,b,x \in D \setminus \{0\}$ , then is it true that $\gcd (ax,bx)=x \cdot \gcd (a,b)$?
112345
In an Integral Domain is it true that $\gcd(ac,ab) = a\gcd(c,b)$?
14693
$d = \gcd(c,m),\ ac≡bc\pmod{\! m}\Rightarrow a≡b\pmod {\!m/d}\ $ [Congruence Cancellation & Division Rule]
126280
In a P.I.D., if $a^m = b^m$ and $a^n = b^n$ for $m, n \in \mathbb{N}$ with $\gcd(m,n) = 1$, then $a=b$
56612
Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
33233
Need to prove that $(S,\cdot)$ defined by the binary operation $a\cdot b = a+b+ab$ is an abelian group on $S = \Bbb R \setminus \{-1\}$.
5789
$ d = \gcd(a,b)\Rightarrow\ \gcd(a/d,b/d) = 1$
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
25825
Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
29452
Divisor in $\mathbb{C}[X]$ $\implies$ divisor in $\mathbb{R}[X]$?
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
20003
Prove for positive integers a,b,c and d (where b does not equal d), if gcd(a,b) = gcd(c,d) = 1, then a/b + c/d is not an integer
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $