Integral domain( not merely $\mathbb{Z}$ ). Prove that $\gcd(ca, cb) = c\gcd(a, b)$
112345
In an Integral Domain is it true that $\gcd(ac,ab) = a\gcd(c,b)$?
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
110726
Example of a non-gcd domain
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
104068
Prove that $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$
14693
$d = \gcd(c,m),\ ac≡bc\pmod{\! m}\Rightarrow a≡b\pmod {\!m/d}\ $ [Congruence Cancellation & Division Rule]
96132
$R$ integral domain : $u\in R^*, a \text{ is prime} \iff au \text{ is prime}$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
60842
if $a^2+b^2=c^2$ then $gcd(a,b)=gcd(a,c)=gcd(b,c)$.
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
55673
Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
7090
Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$
78031
$c\mid a,b\iff c\mid\gcd(a,b)$ [GCD Universal Property]
132193
Why $\Bbb Z$ = (integers) is an integral domain?