Difference between revisions of "Reduced system of residues"
From Encyclopedia of Mathematics
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| − | ''reduced residue system, modulo | + | {{TEX|done}} |
| + | ''reduced residue system, modulo $m$'' | ||
| − | A set of numbers from a [[Complete system of residues|complete system of residues]] modulo | + | 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. |
Revision as of 17:02, 11 April 2014
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.
How to Cite This Entry:
Reduced system of residues. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reduced_system_of_residues&oldid=13499
Reduced system of residues. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reduced_system_of_residues&oldid=13499
This article was adapted from an original article by S.A. Stepanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article