Complete system of residues

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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.


See also Reduced system of residues.

How to Cite This Entry:
Complete 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