Definition:Pairwise Coprime

Definition

GCD Domain

Let $\struct {D, +, \times}$ be a GCD domain.

A subset $S \subseteq D$ is pairwise coprime (in $D$) if and only if:

$\forall x, y \in S: x \ne y \implies x \perp y$

where $x \perp y$ denotes that $x$ and $y$ are coprime.

Euclidean Domain

Let $\struct {D, +, \times}$ be a Euclidean domain.

A subset $S \subseteq D$ is pairwise coprime (in $D$) if and only if:

$\forall x, y \in S: x \ne y \implies x \perp y$

where $x \perp y$ denotes that $x$ and $y$ are coprime.

Integers

A set of integers $S$ is pairwise coprime if and only if:

$\forall x, y \in S: x \ne y \implies x \perp y$

where $x \perp y$ denotes that $x$ and $y$ are coprime.