Mersenne numbers and Fermat numbers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2022]
|
| Schriftenreihe: | Selected chapters of number theory: special numbers
vol. 1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xx, 306 Seiten |
| ISBN: | 9789811230318 |
Internformat
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Datensatz im Suchindex
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| adam_text | Contents Notations ix Preface xv 1. Preliminaries 1.1 1.2 1.3 1.4 1.5 1.6 1.7 2. 1 Divisibility of integers.................................................. Modular arithmetics..................................................... Arithmetic functions..................................................... Solution of congruences .................................. Quadratic residues, Legendre symboland Jacobi symbol................................................................. Multiplicative orders, primitive roots and indexes.................................................................... Continued fractions........................................................ Prime numbers 2.1 2.2 2.3 2.4 2.5 2.6 1 8 11 16 26 29 33 39 History of the question.................................................. 39 Elementary properties of prime numbers.......................43 How to recognize whether a natural number is a prime?....................................................................... 46 Formulas of primes........................................................ 62 Prime numbers in the family of specialnumbers ... 74 Open problems.............................................................. 87 vii
viii 3. Mersenne Numbers and Fermat Numbers Mersenne numbers 3.1 3.2 3.3 3.4 3.5 3.6 History of the question.................................................... 101 Elementary properties of Mersenne numbers...............109 Mersenne primes: Prime divisors of Mersenne numbers.............................................................................118 Mersenne primes: Lucas-Lehmer test............................ 123 Mersenne numbers in the family of special numbers.............................................................................131 Open problems................................................................ 141 4. Fermat numbers 4.1 4.2 4.3 4.4 4.5 4.6 5.3 5.4 5.5 5.6 149 History of the question.................................................... 149 Elementary properties of Fermatnumbers....................156 Fermat primes: Prime divisors of Fermat numbers.............................................................................170 Fermat primes: Pepin’s test...........................................176 Fermat numbers in the family of special numbers.............................................................................181 Open problems.................................................................190 5. Modern Applications 5.1 5.2 101 195 On place of prime numbers in Mathematics.............195 Problems in Number Theory, connected with Mersenne numbers.......................................................... 202 Problems in Number Theory, connected with Fermat numbers................................................................ 211 Prime
numbers records and Mersennenumbers . . . 218 Mersenne and Fermat numbers inCryptography . . 224 Open problems....................................................... 240 6. Zoo of Numbers 249 7. Mini Dictionary 259 8. Exercises 267 Bibliography 295 Index 303
|
| adam_txt |
Contents Notations ix Preface xv 1. Preliminaries 1.1 1.2 1.3 1.4 1.5 1.6 1.7 2. 1 Divisibility of integers. Modular arithmetics. Arithmetic functions. Solution of congruences . Quadratic residues, Legendre symboland Jacobi symbol. Multiplicative orders, primitive roots and indexes. Continued fractions. Prime numbers 2.1 2.2 2.3 2.4 2.5 2.6 1 8 11 16 26 29 33 39 History of the question. 39 Elementary properties of prime numbers.43 How to recognize whether a natural number is a prime?. 46 Formulas of primes. 62 Prime numbers in the family of specialnumbers . 74 Open problems. 87 vii
viii 3. Mersenne Numbers and Fermat Numbers Mersenne numbers 3.1 3.2 3.3 3.4 3.5 3.6 History of the question. 101 Elementary properties of Mersenne numbers.109 Mersenne primes: Prime divisors of Mersenne numbers.118 Mersenne primes: Lucas-Lehmer test. 123 Mersenne numbers in the family of special numbers.131 Open problems. 141 4. Fermat numbers 4.1 4.2 4.3 4.4 4.5 4.6 5.3 5.4 5.5 5.6 149 History of the question. 149 Elementary properties of Fermatnumbers.156 Fermat primes: Prime divisors of Fermat numbers.170 Fermat primes: Pepin’s test.176 Fermat numbers in the family of special numbers.181 Open problems.190 5. Modern Applications 5.1 5.2 101 195 On place of prime numbers in Mathematics.195 Problems in Number Theory, connected with Mersenne numbers. 202 Problems in Number Theory, connected with Fermat numbers. 211 Prime
numbers records and Mersennenumbers . . . 218 Mersenne and Fermat numbers inCryptography . . 224 Open problems. 240 6. Zoo of Numbers 249 7. Mini Dictionary 259 8. Exercises 267 Bibliography 295 Index 303 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T17:55:47Z |
| indexdate | 2024-07-10T09:11:35Z |
| institution | BVB |
| isbn | 9789811230318 |
| language | English |
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| physical | xx, 306 Seiten |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | World Scientific |
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| series | Selected chapters of number theory: special numbers |
| series2 | Selected chapters of number theory: special numbers |
| spelling | Deza, Elena 1961- Verfasser (DE-588)1027553648 aut Mersenne numbers and Fermat numbers Elena Deza, Moscow State Pedagogical University, Russia New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2022] © 2022 xx, 306 Seiten txt rdacontent n rdamedia nc rdacarrier Selected chapters of number theory: special numbers vol. 1 Fermat-Zahl (DE-588)4672709-7 gnd rswk-swf Mersenne-Zahl (DE-588)124515835X gnd rswk-swf Fermat-Zahl (DE-588)4672709-7 s Mersenne-Zahl (DE-588)124515835X s DE-604 Erscheint auch als Online-Ausgabe 978-981-123-032-5 Erscheint auch als Online-Ausgabe 978-981-123-033-2 Selected chapters of number theory: special numbers vol. 1 (DE-604)BV047513069 1 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032818099&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Deza, Elena 1961- Mersenne numbers and Fermat numbers Selected chapters of number theory: special numbers Fermat-Zahl (DE-588)4672709-7 gnd Mersenne-Zahl (DE-588)124515835X gnd |
| subject_GND | (DE-588)4672709-7 (DE-588)124515835X |
| title | Mersenne numbers and Fermat numbers |
| title_auth | Mersenne numbers and Fermat numbers |
| title_exact_search | Mersenne numbers and Fermat numbers |
| title_exact_search_txtP | Mersenne numbers and Fermat numbers |
| title_full | Mersenne numbers and Fermat numbers Elena Deza, Moscow State Pedagogical University, Russia |
| title_fullStr | Mersenne numbers and Fermat numbers Elena Deza, Moscow State Pedagogical University, Russia |
| title_full_unstemmed | Mersenne numbers and Fermat numbers Elena Deza, Moscow State Pedagogical University, Russia |
| title_short | Mersenne numbers and Fermat numbers |
| title_sort | mersenne numbers and fermat numbers |
| topic | Fermat-Zahl (DE-588)4672709-7 gnd Mersenne-Zahl (DE-588)124515835X gnd |
| topic_facet | Fermat-Zahl Mersenne-Zahl |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032818099&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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