算术基本定理
算术基本定理，又称为正整数的唯一分解定理，即：每个大于1的自然数均可写为质数的积，而且这些素因子按大小排列之后，写法仅有一种方式。例如:
，
。
算术基本定理的内容由两部分构成：
- 分解的存在性：
- 分解的唯一性，即若不考虑排列的顺序，正整数分解为素数乘积的方式是唯一的。
算术基本定理是初等数论中一个基本的定理，也是许多其他定理的逻辑支撑点和出发点。
Fundamental theorem of arithmetic
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Fundamental theorem of arithmetic 算术基本定理
![The unique factorization theorem was proved by Gauss with his 1801 book Disquisitiones Arithmeticae.[1] In this book, Gauss used the fundamental theorem for proving the law of quadratic reciprocity.[2]](/uploads/202501/14/Disqvisitiones-8000920.jpg)
In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is prime itself or is the product of prime numbers, and that this product is unique, up to the order of the factors. For example,
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