Definition:Coprime Residue Class

Definition

Let $m \in \Z: m \ge 1$.

Let $a \in \Z$ such that:

$a \perp m$

where $\perp$ denotes that $a$ is prime to $m$.

Let $\eqclass a m$ be the residue class of $a$ (modulo $m$):

$\set {x \in \Z: \exists k \in \Z: x = a + k m}$

Then $\eqclass a m$ is referred to as a coprime residue class.

Also known as

A coprime residue class is also known as a relatively prime residue class.

Sources

• 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 1$. Rings and Fields: Example $4$