### 基本信息

- 原书名：Elementary Number Theory (6th Edition)
- 原出版社： Addison Wesley

- 作者：
**(美)Kenneth H. Rosen** - 丛书名：
**华章统计学原版精品系列** - 出版社：机械工业出版社
- ISBN：
**9787111317982** - 上架时间：2011-5-20
- 出版日期：2010 年9月
- 开本：16开
- 页码：752
- 版次：6-1
- 所属分类：数学 > 代数，数论及组合理论 > 综合

教材

### 编辑推荐

本书是数论课程的经典教材，自出版以来，深受读者好评，被美国加州大学伯克利分校、伊利诺伊大学、得克萨斯大学等数百所名校采用。 <BR>本书以经典理论与现代应用相结合的方式介绍了初等数论的基本概念和方法，内容包括整除、同余、二次剩余、原根以及整数的阶的讨论和计算。

### 内容简介

### 作译者

### 目录

### 前言

This book is ideal for an undergraduate number theory course at any level. No formal prerequisites beyond college algebra are needed for most of the material, other than some level of mathematical maturity. This book is also designed to be a source book for elementary number theory; it can serve as a useful supplement for computer science courses and as a primer for those interested in new developments in number theory and cryptography. Because it is comprehensive, it is designed to serve both as a textbook and as a lifetime reference for elementary number theory and its wide-ranging applications.

This edition celebrates the silver anniversary of this book. Over the past 25 years,close to 100,000 students worldwide have studied number theory from previous editions.Each successive edition of this book has benefited from feedback and suggestions from many instructors, students, and reviewers. This new edition follows the same basic approach as all previous editions, but with many improvements and enhancements. I invite instructors unfamiliar with this book, or who have not looked at a recent edition, to carefully examine the sixth edition. I have confidence that you will appreciate the rich exercise sets, the fascinating biographical and historical notes, the up-to-date coverage, careful and rigorous proofs, the many helpful examples, the rich applications, the support for computational engines such as Maple and Mathematica, and the many resources available on the Web.

Changes in the Sixth Edition

The changes in the sixth edition have been designed to make the book easier to teach and learn from, more interesting and inviting, and as up-to-date as possible. Many of these changes were suggested by users and reviewers of the fifth edition. The following list highlights some of the more important changes in this edition.

~ New discoveries

This edition tracks recent discoveries of both a numerical and a theoretical nature. Among the new computational discoveries reflected in the sixth edition are four Mersenne primes and the latest evidence supporting many open conjectures. The Tao-Green theorem proving the existence of arbitrarily long arithmetic progressions of primes is one of the recent theoretical discoveries described in this edition.

~ Biographies and historical notes

Biographies of Terence Tao, Etienne Bezout, Norman MacLeod Ferrers, Clifford Cocks, and Waclaw Sierpifiski supplement the already extensive collection of biographies in the book. Surprising information about secret British cryptographic discoveries predating the work of Rivest, Shamir, and Adleman has been added.

~ Conjectures

The treatment of conjectures throughout elementary number theory has been expanded, particularly those about prime numbers and diophantine equations. Both resolved and open conjectures are addressed.

~ Combinatorial number theory

A new section of the book covers partitions, a fascinating and accessible topic in combinatorial number theory. This new section introduces such important topics as Ferrers diagrams, partition identies, and Ramanujan's work on congruences. In this section, partition identities, including Euler's important results, are proved using both generating functions and bijections.

~ Congruent numbers and elliptic curves

A new section is devoted to the famous congruent number problem, which asks which positive integers are the area of a right triangle with rational side lengths. This section contains a brief introduction to elliptic curves and relates the congruent number problem to finding rational points on certain elliptic curves. Also, this section relates the congruent number problem to arithmetic progressions of three squares.

~ Geometric reasoning

This edition introduces the use of geometric reasoning in the study of diophantine problems. In particular, new material shows that finding rational points on the unit circle is equivalent to finding Pythgaorean triples, and that finding rational triangles with a given integer as area is equivalent to finding rational points on an associated elliptic curve.

~ Cryptography

This edition eliminates the unnecessary restriction that when the RSA cryptosystem is used to encrypt a plaintext message this message needs to be relatively prime to the modulus in the key.

~ Greatest common divisors