fundamental theorem of arithmetic

算术基本定理

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

Other names / variants: unique prime factorization of positive integers

Translation evidence: Literature usage

Meaning in context

Every integer greater than one is a finite product of positive primes, unique up to the order of its factors.

每个大于 11 的整数都可分解为有限个正素数的乘积，且除因子次序外此分解唯一。

Example

84=22⋅3⋅784=2^2\cdot3\cdot7.

Usage and distinctions

Existence of irreducible factorizations alone is weaker than uniqueness; general domains need not satisfy this theorem.

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Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source唯一分解性, definition def:UFD and following paragraph specializing to Z and naming 算术基本定理 · 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，paragraph following def:UFD identifying Z as UFD and naming 算术基本定理 · Checked 2026-10-14
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