Difference between revisions of "Reduced system of residues"
From Encyclopedia of Mathematics
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''reduced residue system, modulo $m$'' | ''reduced residue system, modulo $m$'' | ||
| − | A set of numbers from a [[ | + | 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|Euler function]]). One usually takes the numbers mutually prime with $m$ in the complete residue system $0,\ldots,m-1$ as reduced residue system. |
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| + | A reduced residue system forms a [[group]] under multiplication modulo $m$. | ||
Latest revision as of 12:45, 23 November 2014
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=31522
Reduced system of residues. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reduced_system_of_residues&oldid=31522
This article was adapted from an original article by S.A. Stepanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article