Fundamentals of number theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass. [u.a.]
Addison-Wesley
1977
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 280 S. Ill. |
| ISBN: | 0201042878 |
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MARC
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| 245 | 1 | 0 | |a Fundamentals of number theory |c William J. LeVeque |
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Record in the Search Index
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| adam_text | Contents
Chapter 1 Introduction
1.1 What is number theory? 1
1.2 Algebraic properties of the set of integers 8
1.3 Types of proofs, and some examples 13
1.4 Representation systems for the integers 18
1.5 The early history of number theory 25
Chapter 2 Unique Factorization and the GCD
2.1 The greatest common divisor 31
2.2 Unique factorization in other domains 35
2.3 The linear Diophantine equation 40
2.4 The least common multiple 44
Chapter 3 Congruences and the Ring Zm
3.1 Congruence and residue classes 47
3.2 Complete and reduced residue systems; Euler s ^ function .... 51
3.3 Linear congruences 58
3.4 Higher degree polynomial congruences 63
3.5 The /7 adic fields 70
Chapter 4 Primitive Roots and the Group Um
4.1 Primitive roots 79
4.2 The structure of Um 86
4.3 nth power residues 90
4.4 An application to Fermat s equation 93
T
vi Contents
Chapter 5 Quadratic Residues
5.1 Introduction 97
5.2 Quadratic residues of primes, and the Legendre symbol 99
5.3 The law of quadratic reciprocity 103
5.4 The Jacobi symbol 109
5.5 Factorization of large integers 113
Chapter 6 Number Theoretic Functions and the Distribution of Primes
6.1 Introduction 121
6.2 The Mobius function 127
6.3 The function [x] 131
6.4 The symbols O , o , « , and ~ 133
6.5 The sieve of Eratosthenes 139
6.6 Sums involving primes 143
6.7 The true order of n(x) 148
6.8 Primes in arithmetic progressions 154
6.9 Bertrand s hypothesis 159
6.10 The order of magnitude of p, a, and x 163
6.11 Average order of magnitude 167
6.12 Brun s theorem on twin primes 173
Chapter 7 Sums of Squares
7.1 Preliminaries 179
7.2 Primitive representations as a sum of two squares 181
7.3 The total number of representations 184
7.4 Sums of three squares 187
7.5 Sums of four squares 187
7.6 Waring s problem 189
Chapter 8 Quadratic Equations and Quadratic Fields
8.1 Legendre s theorem 191
8.2 Pell s equation 198
8.3 Algebraic number fields and algebraic integers 207
8.4 Arithmetic in quadratic fields 212
Chapter 9 Diophantine Approximation
9.1 Farey sequences and Hurwitz s theorem 219
9.2 Best approximations to a real number 226
9.3 Infinite continued fractions 234
9.4 Quadratic irrationalities 239
9.5 Applications to Pell s equation and to factorization 245
Contents vii
9.6 Equivalence of numbers 248
9.7 The transcendence of e 255
Bibliography 260
Appendix 265
Factor Table 266
Computer Plotted Graphs 268
Table of Indices 270
Greek Alphabet 274
List of Symbols 275
Index 277
|
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| indexdate | 2024-07-09T15:42:52Z |
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| isbn | 0201042878 |
| language | English |
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| spelling | LeVeque, William J. Verfasser aut Fundamentals of number theory William J. LeVeque Reading, Mass. [u.a.] Addison-Wesley 1977 VII, 280 S. Ill. txt rdacontent n rdamedia nc rdacarrier Nombres, Théorie des Teoria Dos Numeros larpcal Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001482510&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | LeVeque, William J. Fundamentals of number theory Nombres, Théorie des Teoria Dos Numeros larpcal Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 |
| title | Fundamentals of number theory |
| title_auth | Fundamentals of number theory |
| title_exact_search | Fundamentals of number theory |
| title_full | Fundamentals of number theory William J. LeVeque |
| title_fullStr | Fundamentals of number theory William J. LeVeque |
| title_full_unstemmed | Fundamentals of number theory William J. LeVeque |
| title_short | Fundamentals of number theory |
| title_sort | fundamentals of number theory |
| topic | Nombres, Théorie des Teoria Dos Numeros larpcal Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Nombres, Théorie des Teoria Dos Numeros Number theory Zahlentheorie |
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