Definition:Coprime/Integers

Definition
Let $a$ and $b$ be integers.

Let $\gcd \set {a, b}$ denote the greatest common divisor of $a$ and $b$.

Then $a$ and $b$ are coprime :
 * $\gcd \set {a, b}$ exists

and:
 * $\gcd \set {a, b} = 1$.



Also see

 * Definition:Pairwise Coprime Integers


 * Coprime Integers cannot Both be Zero where it is made explicit that coprimality cannot happen if $a = b = 0$


 * Coprimality Relation is Non-Reflexive: $\neg a \perp a$ except when $a = \pm 1$


 * Coprimality Relation is Symmetric: $a \perp b \iff b \perp a$


 * Coprimality Relation is not Antisymmetric: $\neg \paren {a \perp b \land b \perp a \implies a = b}$


 * Coprimality Relation is Non-Transitive: for example $2 \perp 3, 3 \perp 4, \neg 2 \perp 4$, and also $2 \perp 3, 3 \perp 5, 2 \perp 5$