数论概论（英文版•第3版）——经典原版书库

本书面向非数学专业学生，讲述了有关数论的知识，教给他们如何用数学方法思考问题，同时介绍了目前数学研究的前沿课题。本书采用轻松的写作风格，并包括大量数值示例。对于定理的证明，则强调证明方法而不仅仅是至特定的结果。

Joseph H·Silverman 拥有哈佛大学博士学位。他目前为布朗大学数学教授，之前曾任教于麻省理工学院和波士顿大学。1998年，他获得了美国数学会Stee卜奖的著述奖，获奖著作为《The Arithmetic of Elliptic Curves》 和 《Advanced Topics in the Arithmetic of EllipticCurves》。

Preface
Introduction
l What Is Number Theory?
2 Pythagorean Triples
3 Pythagorean Triples and the Unit Circle
4 Sums of Higher Powers and Fermat,s Last Theorem
5 DiViSibiliwapdthCGfCatCStCOmmOfiD1V1SOf
6 Linear Equations and the Greatest Common Divisor
7 Factorization and the Fundamental Theorem of Arithmetic
8 Congruences
9 Congruences, Powers, and Fermat,s Little Theorem
10 Conmlences, Powers, and Euler's Formula
11 Euler,s Phi Function and the Chinese Remaiiider Theorem
l2 Prime Numbers
l3 Counting Primes
l4 Mersenne Primes
l5 Mersenne Primes and Perfect Numbers
16 Powers Modulo rn and Successive Squaring
l7 Computing hh Roots Modulo rn
l8 Powers, Roots, and.Unbreakable,, Codes
19 PiinalitV TCStillg sfid CthChAnl NUdsfS
20 Euler,s Phi Function and Sums of Divisors
2l Powers Modulo p and Primitive Roots
22 Primitive Roots and Indices
23 Squares Modulo p
24 Is _1 a Square Modulop? Is 2?
25 Quadratic Reciprocity
26 Which Primes Are Sums of TWo Squares?
27 Which Numbers Are Sums of TWo Squares?
28 The Equatioll X4＋Y4＝z4
29 Square-Triangular Numbers Revisited
30 Pell,s Equation
3l Diophantine Approximation
32 Diophantine Approximation and Pell,s Equation
33 Number Theory and Imaginary Numbers
34 The Gaussian Integers and Unique Factorization
35 Irrational Numbers and Transcendenta1 Numbers
36 Binomial Coef6cients and Pascal,s Triangle
37 Fibonacci,s Rabbits and Linear Recurrence Sequences
38 Oh，hata Beautiful Function
39 The Topsy-Turvy World of Continued Fractions
40 Continued Fractions, Square Roots, and Pell,s Equation
4l Generating Functions
42 Sums of Powers
43 Cubic Curves and Elliptic Curves
44 Elliptic Curves with Few Rational Points
45 Points on Elliptic Curves Modulo p
46 Torsion Collections Modulo p and Bad Primes
47 Defect Bounds and Modularity Patterns
48 Elliptic Curves and Fermat,s Last Theorem Further Reading
A Factorization of Small Composite Integers
B A List of Primes
Index