# Definition:Coprime Residue Class

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## 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 $4$