complete residue system

完全剩余系

Number Theory · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: complete system of residues

Translation evidence: Literature usage

Meaning in context

For m≥1m\ge1, a set of integers containing exactly one representative of every congruence class modulo mm.

对正整数 mm，从每个模 mm 剩余类恰取一个整数代表所组成的集合。

Example

{−2,−1,0,1,2}\{-2,-1,0,1,2\} is a complete residue system modulo 55.

Usage and distinctions

Representatives need not lie in the least nonnegative range; the classes, rather than their chosen representatives, are canonical.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Keith Conrad — Modular Arithmetic, University of Connecticut author notesTheorem 2.4, Definition 2.8 and Example 3.11, representatives of all congruence classes · Checked 2026-10-14

Translation sources

  1. 新乡学院数学与统计学院 — 初等数论课程教学大纲第三章，第二节 剩余类及完全剩余系 (PDF page 4); name evidence only · Checked 2026-10-15
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