# Complete system of residues

From Encyclopedia of Mathematics

2010 Mathematics Subject Classification: *Primary:* 11A07 [MSN][ZBL]

*modulo $m$*

Any set of $m$ integers that are incongruent $\bmod\,m$. Usually, as a complete residue system $\bmod\,m$ one takes the least non-negative residues $0,\ldots,m-1$, or the absolutely least residues consisting of the number $0,\pm1,\ldots,\pm(m-1)/2$ if $m$ is odd or the numbers $0,\pm1,\ldots,\pm(m-2)/2,m/2$ if $m$ is even.

#### Comments

See also Reduced system of residues.

**How to Cite This Entry:**

Complete system of residues.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Complete_system_of_residues&oldid=34894

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