摘要数学活动的本身就是离不开解题的，掌握数学知识的一个重要标志就是能够善于解题。而在解题活动中有意识的比赛或者无意识的竞争由来己久。数学竞赛本身就是一种数学活动，是解决数学难题而产生的。最初的数学竞赛至少可以追溯到16世纪初。而初等数论知识是数学竞赛中的重要一环。71620

    初等数论是最古老的数学分支之一，主要研究数的规律、整数性质，它是数论的一个分支，其中古希腊人对数论的发展做出特别了重大的贡献。

初等数论基础知识较简单，但在处理问题方面技巧性比较强，在培养人们思维能力方面有着非常重要作用，所以它在国内外数学竞赛中占有比较重要的位置。数论的发展有着较长的历史，数论和其思想又是数学竞赛中的重要一部分，不管是中小学数学竞赛，或是IMO中，数论的思想都是重点。数学竞赛是数学教育的重要组成部分，对学生的数学思维有着重大的提高作用。

Abstract Mathematics activity itself is the problem can not be separated from the problem， to master the knowledge of mathematics is an important symbol to be able to be good at solving problems. And in the problem solving activities in the consciousness of competition or unconscious competition origin has long. Mathematics competition is a kind of mathematics activity， which is to solve the problem of mathematics. The original mathematical contest dates back at least sixteenth Century. The knowledge of elementary number theory in mathematics competition is an important part of. 

The number of primary branches of mathematics can be said to be one of the oldest properties， main research and the relationship between the integer. Number theory has a long history of development， made an important contribution to the development of the logarithm of the ancient Greeks. 

Basic knowledge of elementary number theory is relatively simple， but very strong skills in dealing with problems， people are thinking ability plays an important role in cultivating， so in the domestic and international mathematics competition occupies an important position. There is a long history about the development of number theory， number theory and the thinking is mathematics competition is the most important part of， no matter is primary school mathematics competition， mathematics competition of junior high school or high school mathematics competition， or the IMO， the number of ideas are the focus of. Mathematics competition is an important part of the current mathematics education， and it plays an important role in improving the students' mathematical thinking.

毕业论文关键词：数学竞赛; 竞赛数学; 初等数论;IMO;如何应用

Keywords: mathematics competition; theory; elementary number theory; how to apply

目录

一、引言...5

二、关于数学竞赛与竞赛数学6

   （一）数学竞赛.6

 1.国际数学奥林匹克的发展.6

 2.中国数学竞赛的发展.6

         3. 数学竞赛的目的8

   （二）竞赛数学.9

 1.竞赛数学的方法与内容...9

 2.竞赛数学的特征.9

 3.竞赛数学的命题10

         4.竞赛数学的解题10

   （三）几个著名定理介绍10

1.孙子定理...10

2.费马大定理.10

3.哥德巴赫猜想..11        4.黎曼猜想...11

三、初等数论思想在数学竞赛中的应用...12

   （一）数学竞赛中的主要初等数论内容12

   （二）与初等数论有关的竞赛题应用举例..12

        1.奇偶性问题.12