An introduction to number theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chicago
Markham
1971
|
| Ausgabe: | 2. print. |
| Schriftenreihe: | Markham mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 347 S. |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804133190097436672 |
|---|---|
| adam_text | CONTENTS
PREFACE v
Chapter 1 AN INTRODUCTION TO NUMBER THEORY 1
1.1 An Introduction to Number Theory 1
1.2 Some Elementary Properties of Divisibility 11
Chapter 2 THE EUCLIDEAN ALGORITHM AND UNIQUE
FACTORIZATION 16
2.1 The Euclidean Algorithm 16
2.2 The Fundamental Theorem of Arithmetic 26
2.3 Applications of the Fundamental Theorem 33
2.4 Multiplicative Functions 36
2.5 Linear Diophantine Equations 44
Chapter 3 CONGRUENCES 51
3.1 Introduction 51
3.2 Fundamental Properties of Congruences 54
3.3 Linear Congruence Equations 66
3.4 Reduced Residue Systems and Euler s $ Function 77
3.5 More on Euler s 4 Function 82
3.6 Polynomial Congruences 86
3.7 Primitive Roots 97
Chapter 4 MAGIC SQUARES 118
4.1 The Uniform Step Method 118
4.2 Filled and Magic Squares 123
4.3 Diabolic and Symmetric Squares 132
4.4 Historical Comments 137
ix
X CONTENTS
Chapter 5 DIOPHANTINE EQUATIONS 145
5.1 Introduction 145
5.2 The Use of Congruences in Solving Diophantine
Equations 148
5.3 Pythagorean Triples 151
5.4 Fermat s Method of Descent 155
Chapter 6 NUMBERS, RATIONAL AND IRRATIONAL 164
6.1 Rational Numbers 164
6.2 Irrational Numbers 170
6.3 Liouville s Theorem and Transcendental Numbers 172
Chapter 7 CONTINUED FRACTIONS FROM A
GEOMETRIC VIEWPOINT 181
7.1 Introduction 181
7.2 The Continued Fraction Algorithm 185
7.3 Computation of an 196
7.4 The Best Approximations 209
7.5 A Commentary of Proof by Picture 223
7.6 Periodic Continued Fractions 226
7.7 The Fermat Pell Equation and the Continued
Fraction Expansion of yjd 239
Chapters QUADRATIC FIELDS 257
8.1 Introduction 257
8.2 Quadratic Fields and Quadratic Integers 258
8.3 Divisibility and Factorization into Primes 270
8.4 Unique Factorization and Euclidean Domains 281
8.5 Applications of Quadratic Fields to Diophantine
Equations 299
8.6 Historical Comments 305
Appendix A TWO DIMENSIONAL VECTORS 317
Appendix B TWO BY TWO MATRICES 322
Appendix C FIELDS 331
BIBLIOGRAPHY 334
ANSWERS TO SELECTED EXERCISES 341
LIST OF SYMBOLS 344
INDEX 345
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| discipline | Mathematik |
| edition | 2. print. |
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| indexdate | 2024-07-09T20:04:46Z |
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| language | English |
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| spelling | Stark, Harold M. Verfasser aut An introduction to number theory Harold M. Stark 2. print. Chicago Markham 1971 X, 347 S. txt rdacontent n rdamedia nc rdacarrier Markham mathematics series 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=013055995&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stark, Harold M. An introduction to number theory Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 |
| title | An introduction to number theory |
| title_auth | An introduction to number theory |
| title_exact_search | An introduction to number theory |
| title_full | An introduction to number theory Harold M. Stark |
| title_fullStr | An introduction to number theory Harold M. Stark |
| title_full_unstemmed | An introduction to number theory Harold M. Stark |
| title_short | An introduction to number theory |
| title_sort | an introduction to number theory |
| topic | Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Zahlentheorie |
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