reduced residue system

简化剩余系

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

Other names / variants: reduced system of residues

Translation evidence: Literature usage

Meaning in context

For m≥2m\ge2, a set of integers representing each invertible congruence class modulo mm exactly once.

对 m≥2m\ge2，从每个模 mm 可逆剩余类恰取一个整数代表所组成的集合。

Example

{1,5,7,11}\{1,5,7,11\} is a reduced residue system modulo 1212.

Usage and distinctions

It contains only classes coprime to the modulus, whereas a complete residue system contains every class.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Keith Conrad — Euler's Theorem, University of Connecticut author notesSection 1, printed page 1, modulo-12 representatives and formula (1.1); Section 2, printed pages 2–3, distinct representatives for every unit · Checked 2026-10-15

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，第三节 简化剩余系与欧拉函数 (PDF page 4); name evidence only · Checked 2026-10-15
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