整数的若干性质.doc

本科毕业论文(设计) 摘 要 整数的性质有很多。其在整个初等数论中是非常有研究意义的一部分。把对整数的研究深度剖析，细分到众多的性质研究当中。可以加深对整数性质及整数的认识。这里着重讨论的是数的整除特性及尾数特征、奇数与偶数、约数与倍数及带余除法。这四个性质在整数中是我们较为常见的、常用的，同时在整个数论中也具有相当重要的地位。 并且在中学数学的教学中有着比较广泛的应用基础。文中阐述了以上性质的含义及对个别性质的证明，并通过实例讨论了整数的若干性质涉及到实际生活中的应用以及涉及到中学数学学习方面的应用,使我们对其更加熟悉并能熟练的应用它解决问题。所总结的解题方法在实际解题当中会更加方便快捷。 关键词:整数的性质；奇数与偶数；约数与倍数；带余除法；应用Abstract There are many properties of integers. It is a very meaningful research in the elementary number theory. The depth analysis of the study of integer, subdivision into the nature of many of the study, you can deepen the understanding of the nature of integer and integer. It emphatically discusses the characteristics and features, the number of mantissa is divisible by odd and even number, and multiple and division. The four properties in the integer is we are more common, common, and it has a very important position in the theory of numbers. And has a wide range of applications in the teaching of mathematics in secondary schools. This paper expounds the above nature of meaning and of individual nature of proof, and through example discussed some properties of integers related to real life application and relates to the middle school mathematics learning application, enable us to become more familiar with and skilled in it is applied to solve the problem. The summary of the problem solving method in the actual problem solving which will be more convenient and quick. Keywords: Properties of integers; Odd and even; And a few times; With complementary division; Application目 录 摘 要 I Abstract II 1 整数若干性质的由来 1 2 整数若干性质的基础知识 3 2.1 整数整除的概念 3 2.1.1 数的整除特性 3 2.1.2 数的尾数特征 5 2.2 奇数与偶数的概念 5 2.3 约数与倍数的概念 5 2.3.1 约数 5 2.3.2 倍数 6 2.4 带余除法定理及其证明 6 3 整数若干性质在中学学习中的应用 7 3.1 整除特性及尾数特征的应用 7 3.2 奇数与偶数的应用 9 3.3 约数与倍数的应用 10 3.4 带余除法的应用 11 4 整数若干性质在著名问题中的应用 11 4.1 中国剩余定理 11 4.2 辗转相除问题 12 5 整数若干性质的总述 15 参考文献 16 谢辞 17 从人们对世界有了认知起,便已经开始接触神秘而又深奥的整数世界,它总能让人充满遐想而又望尘莫及，引起人