Elementary theory of numbers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass.
Addison-Wesley
1965
|
| Ausgabe: | 2. print. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Addison-Wesley series in introductory mathematics |
| Beschreibung: | VIII, 132 S. graph. Darst. |
Internformat
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| 245 | 1 | 0 | |a Elementary theory of numbers |
| 250 | |a 2. print. | ||
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| 300 | |a VIII, 132 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804123415835049984 |
|---|---|
| adam_text | CONTENTS
Chapter 1. Introduction 1
1 1 What is number theory? 1
1 2 Foundations 7
1 3 Proofs by induction 10
1 4 Indirect proofs 15
1 5 Radix representation 17
Chapter 2. The Euclidean Algorithm and Its Consequences . 22
2 1 Divisibility 22
2 2 The Euclidean algorithm and greatest common divisor .... 22
2 3 The unique factorization theorem 26
2 4 The linear Diophantine equation 30
2 5 The least common multiple 35
Chapter 3. Congruences 36
3 1 Introduction 36
3 2 Elementary properties of congruences 37
3 3 Residue classes and arithmetic (mod m) 40
3 4 Reduced residue systems and Euler s (^ function 42
3 5 Linear congruences 48
3 6 Polynomial congruences 55
3 7 Quadratic congruences with prime modulus 59
Chapter 4. The Powers of an Integer Modulo m 62
4 1 The order of an integer (mod m) 62
4 2 Integers belonging to a given exponent (mod p) 66
4 3 Indices 69
Chapter 5. Continued Fractions 73
5 1 Introduction 73
5 2 The basic identities 77
5 3 The simple continued fraction expansion of a rational number . . 82
5 4 The expansion of an irrational number 84
5 5 The expansion of quadratic irrationalities 87
5 6 Approximation theorems 91
Chapter 6. The Gaussian Integers 96
6 1 Introduction 96
6 2 Divisibility, units, and primes 97
6 3 The greatest common divisor 99
6 4 The unique factorization theorem in Z[i] 102
6 5 The primes in Z[i] 103
6 6 Another quadratic domain 106
vii
Viii CONTENTS
CHAPTEB 7. DlOPHANTINE EQUATIONS 108
7 1 Introduction 108
7 2 The equation x2 + y2 = z2 108
7 3 The equation x4 + yA = z* 110
7 4 The equation x2 — dy2 — 1 Ill
7 5 The equation x2 — dy2 = — 1 117
7 6 Pell s equation and continued fractions 118
Appendix 123
Answers to Problems 127
Index 131
|
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| indexdate | 2024-07-09T17:29:25Z |
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| language | English |
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| spelling | LeVeque, William J. Verfasser aut Elementary theory of numbers 2. print. Reading, Mass. Addison-Wesley 1965 VIII, 132 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in introductory mathematics Zahlentheorie (DE-588)4067277-3 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 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=005997707&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | LeVeque, William J. Elementary theory of numbers Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4151278-9 |
| title | Elementary theory of numbers |
| title_auth | Elementary theory of numbers |
| title_exact_search | Elementary theory of numbers |
| title_full | Elementary theory of numbers |
| title_fullStr | Elementary theory of numbers |
| title_full_unstemmed | Elementary theory of numbers |
| title_short | Elementary theory of numbers |
| title_sort | elementary theory of numbers |
| topic | Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Zahlentheorie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005997707&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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