初等数论教学中的辩证法——关于素性检验和正整数的素因数分解的一次课程设计  

Dialectic in Teaching of Elementary Number Theory

作　　者：袁兰党[1] 高印芝[1] YUAN Landang;GAO Yinzhi(School of Mathematical Sciences,Hebei Normal University,Hebei International Joint Research Center for Mathematics and Interdisciplinary Science,Shijiazhuang 050024,China)

机构地区：[1]河北师范大学数学科学学院,河北省数学与交叉科学国际联合中心,河北石家庄050024

出　　处：《高等数学研究》2023年第1期92-94,97,共4页Studies in College Mathematics

基　　金：河北师范大学教学改革项目(2022XJJG081)。

摘　　要：本文就两类特殊的数——梅森数和费马数,将广泛应用于素性检验和正整数的素因数分解中的试除法和两类数的自身特点相结合,便有了这两类数的素性检验和素因数分解的更有效的方法,体现了一般和特殊的关系,是辩证法在数论中的体现.In this paper, we focus on two special kinds of numbers—Mersenne number and Fermat number. First, we introduce the trial division method which is widely used in prime test and prime factorization of positive integers, and then discuss the characters of the two kinds of numbers. Finally, we obtain more effective methods of prime testing and prime factorization of these two kinds of numbers, which shows the relation between the general and the particular, and this is the embodiment of dialectics in number theory.

关 键 词：素性检验 素因数分解 梅森数 费马数 

分 类 号：O157[理学—数学]