Reduced system of residues

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.