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A friendly introduction to number theoryPDF|Epub|txt|kindle电子书版本网盘下载

Joseph H Silverman著著
出版社：北京：机械工业出版社
ISBN：7111196112
出版时间：2006
标注页数：434页
文件大小：55MB
文件页数：447页
主题词：数论－教材－英文

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图书目录

Introduction1

1 What Is Number Theory?6

2 Pythagorean Triples13

3 Pythagorean Triples and the Unit Circle20

4 Sums of Higher Powers and Fermat's Last Theorem24

5 Divisibility and the Greatest Common Divisor28

6 Linear Equations and the Greatest Common Divisor35

7 Factorization and the Fundamental Theorem of Arithmetic44

8 Congruences53

9 Congruences,Powers,and Fermat's Little Theorem60

10 Congruences,Powers,and Euler's Formula66

11 Euler's Phi Function and the Chinese Remainder Theorem70

12 Prime Numbers78

13 Counting Primes85

14 Mersenne Primes91

15 Mersenne Primes and Perfect Numbers95

16 Powers Modulo m and Successive Squaring105

17 Computing kth Roots Modulo m112

18 Powers,Roots,and"Unbreakable"Codes117

19 Primality Testing and Carmichael Numbers123

20 Euler's Phi Function and Sums of Divisors134

21 Powers Modulo p and Primitive Roots139

22 Primitive Roots and Indices149

23 Squares Modulo p156

24 Is-1 a Square Modulo p?Is 2?164

25 Quadratic Reciprocity175

26 Which Primes Are Sums of Two Squares?186

27 Which Numbers Are Sums of Two Squares?198

28 The Equation X4+Y4=Z4204

29 Square-Triangular Numbers Revisited207

30 Pell's Equation216

31 Diophantine Approximation222

32 Diophantine Approximation and Pell's Equation232

33 Number Theory and Imaginary Numbers239

34 The Gaussian Integers and Unique Factorization253

35 Irrational Numbers and Transcendental Numbers270

36 Binomial Coefficients and Pascal's Triangle286

37 Fibonacci's Rabbits and Linear Recurrence Sequences297

38 Oh,What a Beautiful Function310

39 The Topsy-Turvy World of Continued Fractions324

40 Continued Fractions,Square Roots,and Pell's Equation340

41 Generating Functions355

42 Sums of Powers365

43 Cubic Curves and Elliptic Curves376

44 Elliptic Curves with Few Rational Points388

45 Points on Elliptic Curves Modulo p395

46 Torsion Collections Modulo p and Bad Primes406

47 Defect Bounds and Modularity Patterns410

48 Elliptic Curves and Fermat's Last Theorem416