Introduction to number theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey
World Scientific Europe Ltd.
[2018]
|
| Series: | Essential textbooks in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis: Seite 243-244 |
| Physical Description: | xiv, 247 Seiten Diagramme |
| ISBN: | 9781786344892 9781786344717 |
Staff View
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Record in the Search Index
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| adam_text | Contents
About the Author v
Acknowledgments vii
Introduction xi
1 Euclid’s Algorithm 1
1.1 Some Examples of Rings................................ 1
1.2 Euclid’s Algorithm...................................... 5
1.3 Invertible Elements Modulo n............................ 9
1.4 Solving Linear Congruences............................. 13
1.5 The Chinese Remainder Theorem.......................... 16
1.6 Prime Numbers.......................................... 19
Hints for Some Exercises.................................... 26
2 Polynomial Rings 27
2.1 Long Division of Polynomials........................... 28
2.2 Highest Common Factors................................. 34
2.3 Uniqueness of Factorization ........................... 38
2.4 Irreducible Polynomials................................ 40
2.5 Unique Factorization Domains........................... 46
Hints for Some Exercises.................................... 50
3 Congruences Modulo Prime Numbers 53
3.1 Fermat’s Little Theorem................................ 55
3.2 The Euler Totient Function ............................ 57
3.3 Cyclotomic Polynomials and Primitive Roots............. 61
3.4 Public Key Cryptography................................ 68
3.5 Quadratic Reciprocity ................................. 73
3.6 Congruences in an Arbitrary Ring....................... 84
ix
X
Introduction to Number Theory
3.7 Proof of the Second Nebensatz........................... 91
3.8 Gauss Sums and the Proof of Quadratic Reciprocity .... 93
Hints for Some Exercises..................................... 99
4 p-Adic Methods in Number Theory 101
4.1 Hensel’s Lemma......................................... 101
4.2 Quadratic Congruences.................................. 112
4.3 p-Adic Convergence of Series........................... 116
4.4 p-Adic Logarithms and Exponential
Maps................................................... 124
4.5 Teichmiiller Lifts .................................... 130
4.6 The Ring of p-Adic Integers............................ 139
Hints for Some Exercises.................................... 148
5 Diophantine Equations and Quadratic Rings 149
5.1 Diophantine Equations and Unique
Factorization.......................................... 149
5.2 Quadratic Rings........................................ 152
5.3 Norm-Euclidean Quadratic Rings........................ 159
5.4 Decomposing Primes in Quadratic Rings.................. 167
5.5 Continued Fractions................................... 176
5.6 Pell’s Equation ....................................... 185
5.7 Real Quadratic Rings and Diophantine Equations......... 193
Hints for Some Exercises.................................... 199
Solution to Exercises 201
Bibliography 243
Index 245
|
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| indexdate | 2024-07-10T08:03:29Z |
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| isbn | 9781786344892 9781786344717 |
| language | English |
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| spelling | Hill, Richard Michael Verfasser (DE-588)1155099125 aut Introduction to number theory Richard Michael Hill New Jersey World Scientific Europe Ltd. [2018] xiv, 247 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Essential textbooks in mathematics Literaturverzeichnis: Seite 243-244 Zahlentheorie (DE-588)4067277-3 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Zahlentheorie (DE-588)4067277-3 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030268957&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hill, Richard Michael Introduction to number theory Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4151278-9 |
| title | Introduction to number theory |
| title_auth | Introduction to number theory |
| title_exact_search | Introduction to number theory |
| title_full | Introduction to number theory Richard Michael Hill |
| title_fullStr | Introduction to number theory Richard Michael Hill |
| title_full_unstemmed | Introduction to number theory Richard Michael Hill |
| title_short | Introduction to number theory |
| title_sort | introduction to number theory |
| topic | Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Zahlentheorie Einführung |
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