《初等数论》教学中的启示及应用

Enlightenment and Applications in the Teaching of Elementary Number Theory

初等数论是一门研究“数”的学科,是针对数学专业的本科生开设的一门课程。本文主要阐述了在初等数论的教学过程中得到的一些启示和应用,分别为以下三方面内容:一是利用同余的性质得到了任意整数b能被给定正整数a整除的等价条件;二是给出了求解任意同余式的方法;三是给出了指数的两种证明方法。Elementary Number Theory is a subject that studies “number” and is a course for undergraduates majoring in mathematics. This paper mainly expounds enlightenment and applications obtained in the teaching process of elementary number theory, which are as follows: First, the equivalent condition that any integer b can be evenly divided by a given positive integer a is obtained by using the property of congruence. Second, the method of solving any congruence formula is given. Third, two methods of proving the index are given.