同余问题讨论-应用数学毕业论文.docxVIP

南京师范大学泰州学院毕业论文（设计）（一五届）题目：同余问题的讨论院（系、部）：数学科学与应用学院专业：数学与应用数学姓名：朱嘉斌学导教师：黄玉才南京师范大学泰州学院教务处制摘要：无论是从理论上还是从应用上来看, 同余理论都是数论中重要的一部分, 初等数论的核心是以同余的性质、 同余的概念为基础发展起来的同余理论, 同余理论是数论所特有的思想, 也是研究余数除法的重要工具。本文首先归纳总结了同余的性质及其应用, 在同余的定义的基础上, 介绍了同余的中几个重要的性质, 并且侧重讨论了同余的几个重要的应用, 剩余类和剩余系也是它的研究对象。然后,又归纳总了同余方程的解及应用, 例如: 一次同余式的形式、解同余式以及解一次同余式组和中国剩余定理的应用等问题, 讨论的过程中由浅入深, 层层推进, 对相关知识的总结形成了较为完整的知识体系, 对解同余方程的一些特殊的性质理解更为深刻。再次, 结合同余理论的概念与性质, 给出常见的习题及解题技巧, 并举例说明了几个重要的同余定理和它们的应用。最后，余数问题是数论知识板块中另一个内容丰富，题目难度较大的知识体系，也是各大杯赛小升初考试必考的奥数知识点，所以学好本讲对于学生来说非常重要。余数问题主要包括了带余除法的定义，三大余数定理（加法余数定理，乘法余数定理，和同余定理），及中国剩余定理和有关弃九法原理的应用。 关键字：同余；剩余系；一次同余式；奥数数论的同余问题Abstract:both theoretically and from the application point of view,congruence theory is an important part of the number theory, the core of elementary number theory is based on the nature of the congruence, developed on the basis of theconcept of congruence congruence theory, the thought of congruence theory is unique to number theory, is also an important tool to study the remainder division. This paper summarized the properties and applications of congruence, on the basis of the definition of congruence, introduced with Yu Dezhong several important properties, and discusses the congruence on several important application of residue class and residue system is its research object. Then, summarized the total congruence equation solution and application, for example: a congruence type, congruence type and solution in the form of a congruence type group and the application of the Chinese remainder theorem, discuss the process of unit 1, layer upon layer, summary of knowledge formed a relatively complete knowledge system, some special properties of solution congruence equation more profound understanding. Again, the concept of combining the theory of congruence and the nature of common problems and problem solving skills, and illustrates several important with Chinese remainder theory and their applications. Finally, the remainder is another rich theory knowledg