关于牛顿一元整系数多项式一次因式寻找法的证明  

A Proof of Newton’s Method for Finding the First Degree Factor of Monovariate Polynomials with Integer Coefficients

作　　者：杨欣童 

机构地区：[1]清华大学科学史系,北京

出　　处：《理论数学》2023年第8期2319-2324,共6页Pure Mathematics

摘　　要：著名数学家牛顿在其数学专著《广义算术》中提出的一元整系数多项式一次因式寻找法简洁新颖,曾受到了莱布尼兹、约翰•伯努利和赫尔曼等多位数学家高度重视。后人对牛顿的这种方法有多种解释,但未见有证明。本文对这种方法进行深入分析,借助现代符号给出了一种严格证明。The famous mathematician Newton proposed a simple and novel method for finding the first-degree factor of a polynomial with integer coefficients in his mathematical monograph Arithmetica Universalis, which has been highly valued by mathematicians such as Leibniz, John Bernoulli, and Hermann. There are various explanations for Newton’s method, but no proof has been found. This article conducts an in-depth analysis of this method and provides rigorous proof using modern symbols.

关 键 词：牛顿 代数 多项式 一次因式 《广义算术》 

分 类 号：G63[文化科学—教育学]