Difference between revisions of "Complete system of residues"
From Encyclopedia of Mathematics
(Importing text file) |
(TeX) |
||
| Line 1: | Line 1: | ||
| − | ''modulo | + | {{TEX|done}} |
| + | ''modulo $m$'' | ||
| − | Any set of | + | 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. |
Revision as of 13:59, 11 August 2014
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