保正版！爱德华·卢卡斯与素性判定9787560392660哈尔滨工业大学出版社(加)休·C.威廉姆斯

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作者: (加)休·C.威廉姆斯
出版社: 哈尔滨工业大学出版社
ISBN: 9787560392660

出版时间: 2021-03
装帧: 平装
开本: 16开

作者: (加)休·C.威廉姆斯
出版社: 哈尔滨工业大学出版社

ISBN: 9787560392660
出版时间: 2021-03

装帧: 平装
开本: 16开

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目录
Table of symbols

Preface

Preliminaries

1.1 Results from elementary number theory

1.2 Algorithms and complexity

1.3 Continued fractions

1.4 Some arithmetic functions

1.5 Results concerning binomial congruences

Notes for Chapter 1

2 The Beginnings

2.1 Antiquity

2.2 From the Middle Ages to Mersenne

2.3 Fermat and Euler

2.4 Lagrange, Legendre, and Gauss

2.5 The early tablemakers

Notes for Chapter 2

3 Lucas Early Work

3.1 Lucas earliest primality tests

3.2 Lucas and M127

Notes for Chapter 3

4 The Lucas Functions

4.1 Definition of the Lucas functions

4.2 Identity properties of the Lucas functions

4.3 Arithmetic properties

4.4 Computation of the Lucas functions

Notes for Chapter 4

5 Lucas Tests

5.1 Lucas early tests for Mersenne primes

5.2 The Fermat numbers

5.3 Landry and F6

5.4 Lucas and necessity

5.5 Lucas extended tests

Notes for Chapter 5

Later Developments

6.1 The work of Proth and Pocklington

6.2 Early factoring methods

6.3 Coles example

6.4 The Fermat numbers

Notes for Chapter 6

Early Devices

7.1 The beginnings of mechanization

7.2 Mechanisms for testing Mersenne numbers

7.3 The number sieve

Notes for Chapter 7

Kraitchik and Lehmer

8.1 Kraitchik

8.2 D.H. Lehmer

8.3 Some spe numbers

8.4 The Lehmer functions

8.5 Some tables

Notes for Chapter 8

9 Finite Fields

9.1 Groups and rings

9.2 Polynomials and fields

9.3 Finite fields

9.4 Some polynomial congruences

Notes for Chapter 9

10 Lucas Functions Generalized

10.1 A generalization of the Lucas functions

10.2 Some identity properties

10.3 Some arithmetic properties

10.4 Some results on Cn

10.5 Primality tests

Notes for Chapter 10

11 Spe Tests for Primality

11.1 Gauss and Jacobi sums

11.2 A primality test

11.3 Some spe cases

Notes for Chapter 11

12 The Influence of the Computer

12.1 Some observations

12.2 Some primality tests

12.3 Some further tests

12.4 A result of Lenstra and R1031

Notes for Chapter 12

13 Results from the Computer

13.1 The Cunningham project

13.2 Primes of the form k2n + 1

13.3 Fast multiplication

13.4 Fermat and Mersenne numbers

Notes for Chapter 13

14 Primality Proofs

14.1 Factoring and primality tests

14.2 The complexity of primality testing

14.3 Certificates of primality

14.4 Introduction to elliptic curves

14.5 Very short certificates of primality

Notes for Chapter 14

15 Probabilistic Primality Tests

15.1 Pseudoprimes and Carmichael numbers

15.2 Stronger pseudoprimes

15.3 Cryptography

15.4 Probabilistic methods

Notes for Chapter 15

16 Recent Sieve Devices

16.1 Modern sieve devices

16.2 Pseudosquares and primality testing

16.3 The search for pseudosquares

16.4 Application to testing primality

Notes for Chapter 16

17 Primality Proving Today

17.1 The APR test

17.2 The Jacobi sums test

17.3 Primality testing with elliptic curves

17.4 The Lucas connection

17.5 Conclusion

Notes for Chapter 17

Bibliography

Index

编辑手记

内容摘要
本书主要包括初等数论的结果，算法与复杂性，卢卡斯的早期工作，卢卡斯函数的定义、等同性，卢卡斯测试，普罗斯和波金顿的工作，机械化的开始，有限域，卢卡斯函数的推广，素性的特殊测定，计算机的影响，素性证明，很近的筛分设备等内容。素数的数学思想具有悠久的历史，在人类意识中占据了一个重要的位置。本书深入浅出的讲解了如何判断一个给定的整数是否是素数，叙述时列举了许多经典题例与图片，定理叙述简洁明了。本书可供相关专业师生使用，也可供相关爱好者阅读。
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