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''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.

[[Category:Number theory]]