Reduced system of residues

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2020 Mathematics Subject Classification: Primary: 11A07 [MSN][ZBL] reduced residue system, modulo $m$

A set of numbers from a complete system of residues modulo $m$ that are mutually prime with $m$. A reduced residue system modulo $m$ consists of $\phi(m)$ numbers, where $\phi(m)$ is Euler's $\phi$-function (cf. Euler function). One usually takes the numbers mutually prime with $m$ in the complete residue system $0,\ldots,m-1$ as reduced residue system.

A reduced residue system forms a group under multiplication modulo $m$.

How to Cite This Entry:
Reduced system of residues. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by S.A. Stepanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article