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.

Lemmas: 1
Proofs: 2 3 4 5 6
Propositions: 7 8 9 10

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  1. Landau, Edmund: "Vorlesungen ├╝ber Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927
  2. Jones G., Jones M.: "Elementary Number Theory (Undergraduate Series)", Springer, 1998