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Difference between revisions of "Reduced system of residues"

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(Category:Number theory)
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''reduced residue system, modulo $m$''
 
''reduced residue system, modulo $m$''
  
A set of numbers from a [[Complete system of residues|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 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.
  
[[Category:Number theory]]
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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=34175
This article was adapted from an original article by S.A. Stepanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article