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初等数论及其应用 第5版PDF|Epub|txt|kindle电子书版本网盘下载
- （美）罗森（Rosen，K.H.）著 著
- 出版社： 北京：机械工业出版社
- ISBN：7111159144
- 出版时间：2005
- 标注页数：722页
- 文件大小：280MB
- 文件页数：740页
- 主题词：初等数论－英文
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图书目录
What Is Number Theory?1
1 The Integers5
1.1 Numbers and Sequences6
1.2 Sums and Products16
1.3 Mathematical Induction23
1.4 The Fibonacci Numbers30
1.5 Divisibility37
2 Integer Representations and Operations43
2.1 Representations of Integers43
2.2 Computer Operations with Integers53
2.3 Complexity of Integer Operations60
3 Primes and Greatest Common Divisors67
3.1 Prime Numbers68
3.2 The Distribution of Primes77
3.3 Greatest CommonDivisors90
3.4 The Euclidean Algorithm97
3.5 The Fundamental Theorem of Arithmetic108
3.6 Factorization Methods and the Fermat Numbers123
3.7 Linear Diophantine Equations133
4 Congruences141
4.1 Introduction to Congruences141
4.2 Linear Congruences153
4.3 The Chinese Remainder Theorem158
4.4 Solving Polynomial Congruences168
4.5 Systems of Linear Congruences174
4.6 Factoring Using the Pollard Rho Method184
5 Applications of Congruences189
5.1 Divisibility Tests189
5.2 The Perpetual Calendar195
5.3 Round-Robin Tournaments200
5.4 Hashing Functions202
5.5 Check Digits207
6 Some Special Congruences215
6.1 Wilson's Theorem and Fermat's Little Theorem215
6.2 Pseudoprimes223
6.3 Euler's Theorem233
7 Multiplicative Functions239
7.1 The Euler Phi-Function239
7.2 The Sum and Number of Divisors250
7.3 Perfect Numbers and Mersenne Primes257
7.4 M？bius Inversion269
8 Cryptology277
8.1 Character Ciphers278
8.2 Block and Stream Ciphers286
8.3 Exponentiation Ciphers305
8.4 Public Key Cryptography308
8.5 Knapsack Ciphers316
8.6 Cryptographic Protocols and Applications323
9 Primitive Roots333
9.1 The Order of an Integer and Primitive Roots334
9.2 Primitive Roots for Primes341
9.3 The Existence of Primitive Roots347
9.4 Index Arithmetic355
9.5 Primality Tests Using Orders of Integers and Primitive Roots365
9.6 Universal Exponents372
10 Applications of Primitive Roots and the Order of an Integer379
10.1 Pseudorandom Numbers379
10.2 The ElGamal Cryptosystem389
10.3 An Application to the Splicing of Telephone Cables394
11 Quadratic Residues401
11.1 Quadratic Residues and Nonresidues402
11.2 The Law of Quadratic Reciprocity417
11.3 The Jacobi Symbol430
11.4 Euler Pseudoprimes439
11.5 Zero-Knowledge Proofs448
12 Decimal Fractions and Continued Fractions455
12.1 Decimal Fractions455
12.2 Finite Continued Fractions468
12.3 Infinite Continued Fractions478
12.4 Periodic Continued Fractions490
12.5 Factoring Using Continued Fractions504
13 Some Nonlinear Diophantine Equations509
13.1 Pythagorean Triples510
13.2 Fermat's Last Theorem516
13.3 Sums of Squares528
13.4 Pell's Equation539
14 The Gaussian Integers547
14.1 Gaussian Integers and Gaussian Primes547
14.2 Greatest Common Divisors and Unique Factorization559
14.3 Gaussian Integers and Sums of Squares570
A Axioms for the Set of Integers577
B Binomial Coefficients581
C Using Maple and Mathematica for Number Theory589
C.1 Using Maple forNumberTheory589
C.2 Using Mathematica for Number Theory593
D Number Theory Web Links599
E Tables601
Answers to Odd-Numbered Exercises617
Bibliography689
Index of Biographies703
Index705
Photo Credits721