coprimality of integers

整数互素

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

Other names / variants: relatively prime integers · coprime integers

Translation evidence: Literature usage

Meaning in context

Integers a,ba,b are coprime when gcd⁡(a,b)=1\gcd(a,b)=1.

两个整数的最大公因数为 11 时，称它们互素。

Example

88 and 1515 are coprime although neither is prime.

Usage and distinctions

For three integers, a joint gcd of one does not imply pairwise coprimality: use 6,10,156,10,15.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Thomas W. Judson — Abstract Algebra: Theory and ApplicationsSection 2.2, relatively prime definition 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，sentence naming 互素 immediately after 最大公因子 definition · Checked 2026-10-14
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