integer divisibility

整数整除

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

Other names / variants: divides · 整除性

Translation evidence: Literature usage

Meaning in context

For integers $a,b$, $a\mid b$ means that $b=ak$ for an integer $k$.

对整数 $a,b$，若存在整数 $k$ 使 $b=ak$，则称 $a$ 整除 $b$。

Example

$-3\mid12$ because $12=(-3)(-4)$.

Usage and distinctions

The order matters: $a\mid b$ means $a$ divides $b$; also $0\mid b$ holds only for $b=0$.

Read the encyclopedia explanation

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Thomas W. Judson — Abstract Algebra: Theory and ApplicationsSection 2.2, divisibility paragraph before Theorem 2.2.2 · Checked 2026-10-14

Translation sources

1. 李文威 — 代数学方法 卷一，作者源文件唯一分解性，opening definition 整除关系 and preceding sentence specializing to Z · Checked 2026-10-14

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