两个多项式整除与其高次幂整除的关系  

Divisibility Relation between Two Polynomials and Their Powers

作　　者：张会平[1] 于洋 ZHANG Huiping;YU Yang(School of Mathematics,Renmin University of China,Beijing 100872,China;Business School,Renmin University of China,Beijing 100872,China)

机构地区：[1]中国人民大学数学学院,北京100872 [2]中国人民大学商学院,北京100872

出　　处：《高等数学研究》2023年第1期16-18,共3页Studies in College Mathematics

基　　金：国家自然科学基金面上项目(11671399)。

摘　　要：对于数域P上的两个一元多项式f(x)与g(x),本文用五种方法证明了由g^(2)(x)整除f^(2)(x)可得到g(x)整除f(x).这些方法运用了不可约多项式、最大公因式、因式分解以及多项式整除的性质,它们也可推广应用于证明高次的情形.This manuscript proves that f^(2)(x) is divisible by g^(2)(x) is equivalent to f(x) is divisible by g(x), where f(x) and g(x) are two one-variable polynomials.Five methods are used based on the properties of irreducible polynomials, the greatest common divisor, relatively prime polynomials, and divisibility, which can also be used to prove the higher power cases.

关 键 词：一元多项式 整除 最大公因式 不可约多项式 因式分解 

分 类 号：O151.1[理学—数学]