Difference between revisions of "Complete system of residues"
From Encyclopedia of Mathematics
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| − | Any set of | + | ''modulo $m$'' |
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| + | 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==== | ====Comments==== | ||
| − | See also [[ | + | See also [[Reduced system of residues]]. |
Latest revision as of 12:43, 23 November 2014
2020 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=15724
Complete system of residues. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Complete_system_of_residues&oldid=15724
This article was adapted from an original article by S.A. Stepanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article