# Reduced system of residues

From Encyclopedia of Mathematics

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: http://encyclopediaofmath.org/index.php?title=Reduced_system_of_residues&oldid=34895

This article was adapted from an original article by S.A. Stepanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article