李联林^*

（  保利科技有限公司；  ）

摘要： 本文依据整除关系式，对于所有的奇数进行了系统地分类。这是一种全新的整数体系，费马数只是某类整除关系式中的一种特例。根据新发现的余数定理，可以构建一种二元二次不定方程，创立一种新的算法来进行因数分解。利用获得的有关不定方程中整数L数值结构的推理或者猜测，对于较大的因数，尤其是费马合数的较大因数，因数分解时的计算效率很高。发现所有属于同一种类型整除关系式的合数，无论它们有多么大，因数和整数L全都具有类似的数值结构，可以根据这种规律来提高现有因数分解算法的效率。
关键词： 初等数论；计算数论；因数分解；费马数

LI Lianlin^*

（  Poly Technologies, Inc.；  ）

Abstract： According to the divisibility relations, all odd numbers are classified systematically in this paper. This is a new system of integer. The Fermat numbers are a few particular cases under one type only. According to a newly discovered Remainder Theorem, we can found a new factorization algorithm for all composite numbers by a binary indefinite quadratic equation. Using an inference and/or some conjectures about the structure of the integer L in this indefinite equation, the efficiency of factorization will be very high to all larger factors, specially for the Fermat numbers. If only the divisibility relations of different composite numbers belong to the same type, no matter how large they are, the strucures of all factors and integers L are analogous. We can use this regular pattern to improve the computational efficiency of the current factorization algorithms.

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