摘    要 随着大学高校自主招生制度的改革和完善，自主招生考试越来越受到考生和家长的重视，数论问题作为考试中的一大热点问题，持续受到关注。而在中学数学竞赛中，数论问题一直占有较大比重。整除理论、最大公约数、最小公倍数、带余数除法、同余方程、不定方程等数论所涉及的内容，是学生在参加此类比赛前所必须掌握的。本文将通过对“华约”、“北约”等自主招生考试以及各类中学数学竞赛中的数论试题进行整理分析研究，对其典型试题进行题型以及解法介绍。85112

With the reform and improvement of college admissions system, Number theory as one of the oldest branches of mathematics, gradually becoming a hot issue in self-enrollment Problems in number theory has always occupied a large proportion in the mathematical competition。 Students must master pisibility, greatest common pisor and least common multiple, pision with remainder, congruence, perfect square, indefinite equation content related to number theory。 In this paper, I have researched some number theory questions in "WTO", "NATO" and other independent admission examination and high school in the competition。 Elementary number theory plays an important role in all kinds of mathematics competitions, and it has an increasing proportion in recent years。 The theory of pisibility, congruence theory and indefinite equation are the darling of high school mathematics competition。 The author gives a brief introduction of the basic knowledge of the three parts。 After that, according to questioning forms of the three parts, the author discusses how to solve them respectively。 Then, based on solutions obtained through the application of elementary number theory and combining knowledge reserve and thinking level of middle school students, the author provides the optimal solution plan for middle school mathematic competitions through case study。

毕业论文关键词：数学竞赛； 自主招生； 整除理论； 同余理论； 不定方程

Keywords: mathematics competitions; college admissions; theory of pisibility; congruence theory; indefinite equation

目    录

摘    要 2

1。 引言 4

1。1 研究背景 4

1。1。1。 数论问题在古代的发展 4

1。1。2。 数论在现代数学竞赛以及我国高校自主招生中的地位 4

1。2 国内外研究现状 4

1。3 研究目的和内容 5

1。3。1。 研究目的 5

1。3。2。 研究内容 5

2。 整除理论 5

2。1 整除理论 5

2。2 整除理论在自主招生源Q于W优H尔J论K文M网WwW.youeRw.com 原文+QQ75201.,8766 及数学竞赛中的应用 7

2。2。1。 整除性质的运用 7

2。2。2。 带余数除法的运用 8

2。2。3。