**Definition**: Reduced Residue System

Let $m > 0$ be a positive integer and let $C=\{a_1,\ldots,a_m\}$ a complete residue system modulo $m$. We call $R$ a **reduced residue system modulo $m$**, if $R$ is a subset $R\subseteq C$ consisting only of those integers, which are co-prime to $m.$

Note: With the Euler function $\phi$, it follows that $R$ has $\phi(m)$ elements.

| | | | | created: 2019-04-19 07:32:41 | modified: 2019-04-19 07:59:03 | by: *bookofproofs* | references: [1272], [8152]

## 1.**Proposition**: Creation of Reduced Residue Systems From Others

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[8152] **Jones G., Jones M.**: “Elementary Number Theory (Undergraduate Series)”, Springer, 1998

[1272] **Landau, Edmund**: “Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie”, S. Hirzel, Leipzig, 1927

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