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初等数论及其应用 英文版·第6版PDF|Epub|txt|kindle电子书版本网盘下载
- （美）罗森著 著
- 出版社： 北京：机械工业出版社
- ISBN：9787111317982
- 出版时间：2010
- 标注页数：752页
- 文件大小：59MB
- 文件页数：767页
- 主题词：初等数论－英文
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图书目录
1 The Integers5
1.1 Numbers and Sequences5
1.2 Sums and Products16
1.3 Mathematical Induction23
1.4 The Fibonacci Numbers30
1.5 Divisibility36
2 Integer Representations and Operations45
2.1 Representations of Integers45
2.2 Computer Operations with Integers54
2.3 Complexity of Integer Operations61
3 Primes and Greatest Common Divisors69
3.1 Prime Numbers70
3.2 The Distribution of Primes79
3.3 Greatest Common Divisors and their Properties93
3.4 The Euclidean Algorithm102
3.5 The Fundamental Theorem of Arithmetic112
3.6 Factorization Methods and the Fermat Numbers127
3.7 Linear Diophantine Equations137
4 Congruences145
4.1 Introduction to Congruences145
4.2 Linear Congruences157
4.3 The Chinese Remainder Theorem162
4.4 Solving Polynomial Congruences171
4.5 Systems of Linear Congruences178
4.6 Factoring Using the Pollard Rho Method187
5 Applications of Congruences191
5.1 Divisibility Tests191
5.2 The Perpetual Calendar197
5.3 Round-Robin Toumaments202
5.4 Hashing Functions204
5.5 Check Digits209
6 Some Special Congruences217
6.1 Wilson's Theorem and Fermat's Little Theorem217
6.2 Pseudoprimes225
6.3 Euler's Theorem234
7 Multiplicative Functions239
7.1 The Euler Phi-Function239
7.2 The Sum and Number of Divisors249
7.3 Perfect Numbers and Mersenne Primes256
7.4 M？bius Inversion269
7.5 Partitions277
8 Cryptology291
8.1 Character Ciphers291
8.2 Block and Stream Ciphers300
8.3 Exponentiation Ciphers318
8.4 Public Key Cryptography321
8.5 Knapsack Ciphers331
8.6 Cryptographic Protocols and Applications338
9 Primitive Roots347
9.1 The Order of an Integer and Primitive Roots347
9.2 Primitive Roots for Primes354
9.3 The Existence of Primitive Roots360
9.4 Discrete Logarithms and Index Arithmetic368
9.5 Primality Tests Using Orders of Integers and Primitive Roots378
9.6 Universal Exponents385
10 Applications of Primitive Roots and the Order of an Integer393
10.1 Pseudorandom Numbers393
10.2 The ElGamal Cryptosystem402
10.3 An Application to the Splicing of Telephone Cables408
11 Quadratic Residues415
11.1 Quadratic Residues and Nonresidues416
11.2 The Law of Quadratic Reciprocity430
11.3 The Jacobi Symbol443
11.4 Euler Pseudoprimes453
11.5 Zero-Knowledge Proofs461
12 Decimal Fractions and Continued Fractions469
12.1 Decimal Fractions469
12.2 Finite Continued Fractions481
12.3 Infinite Continued Fractions491
12.4 Periodic Continued Fractions503
12.5 Factoring Using Continued Fractions517
13 Some Nonlinear Diophantine Equations521
13.1 Pythagorean Triples522
13.2 Fermat's Last Theorem530
13.3 Sums of Squares542
13.4 Pell's Equation553
13.5 Congruent Numbers560
14 The Gaussian Integers577
14.1 Gaussian Integers and Gaussian Primes577
14.2 Greatest Common Divisors and Unique Factorization589
14.3 Gaussian Integers and Sums of Squares599
Appendix A Axioms for the Set of Integers605
Appendix B Binomial Coefficients608
Appendix C Using Maple and Mathematica for Number Theory615
C.1 Using Maple for Number Theory615
C.2 Using Mathematica for Number Theory619
Appendix D Number Theory Web Links624
Appendix E Tables626
Answers to Odd-Numbered Exercises641
Bibliography721
Index of Biographies733
Index735
Photo Credits752