初等数论在中学数学竞赛中的应用
摘要：数学竞赛研究是数学教育研究的一个重要课题，是英才教育的手段之一。而初等数论作为一个古老的数学分支，在培养人们思维能力方面起着重要的作用，因此，数论以及思想是竞赛中相当重要的部分。本文从中学数学竞赛发展及现状入手，介绍初等数论中较为重要的定理、猜想，进一步提炼初等数论中化归、整体、配对数学思想，再则探讨同余理论的应用及不定方程的解法。然后，联系竞赛中的实例，分析有关于数论的主要考查内容及知识点的分布。最后，对初等数论的学习及中学数学竞赛培优提出一些建议和方法。
关键词：中学数学竞赛；初等数论；数学思想；
The Application of Elementary Number Theory in Middle School Mathematics Tournament
WANG Jia-wei Director: ZHU Wei-yi
(College of Mathematics,Physics and Information Engineering, Mathematics and Applied Mathematics, Zhejiang Normal University)
Abstract:Mathematics Competition is an important research topic of mathematics education research, is one of the means of excellence in education.The elementary number theory as an ancient branch of mathematics, plays an important role in the culture of people thinking ability, therefore, number theory and the idea is a very important part of the race.In this paper, the development and Middle School Mathematics Olympiad paper introduces elementary number theory more important theorems, conjecture, and further refinement of the return of elementary number theory, overall, matching mathematical thinking, she then explore the application of solution congruence theory and indeterminate equations.Then, contact contest instance, analysis of the distribution of content on the main test and knowledge of number theory.Finally, the number of elementary and middle school mathematics learning theory contest excellent training to make some suggestions and methods.
Key Word：high school mathematics competition; elementary number theory; mathematical thinking
