If $a$ and $b$ on a UFD don't have any associated irreducible factors, then $1\in GCD(a,b)$
94722
GCD expressed with irreducible elements in a unique factorization domain
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
74224
On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
96398
An integer $a \pmod m$ has inverse if and only if $\gcd(a,m)=1$?
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
63758
$c\mid ab\Rightarrow c\mid \gcd(a,c)\gcd(b,c),\,$ for integers $a, b, c$
37596
If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
83871
GCDs in integral domains are unique up to unit factors (associates)
24413
Why is $\mathbb{Z}[\sqrt{-n}], n\ge 3$ not a UFD?
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
48480
Find two elements that don't have a gcd in a subring of Gaussian integers
44076
Proving if $d_0$ is the smallest positive integer in $S$ then $d_0 = \gcd(a,b)$