Complete residue system
= Complete residue system
{title2=$\{a_1,\ldots,a_m\}\longrightarrow\mathbb Z/m\mathbb Z\text{ bijectively}$}
A complete residue system modulo a positive <integer> $m$ contains exactly one representative of every <congruence class> modulo $m$. Both $\{0,\ldots,m-1\}$ and $\{1,\ldots,m\}$ are examples. Counting the representatives that are <coprime> to $m$ gives <Euler's totient function>; those representatives form a reduced residue system.