Number theory and its history:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
McGraw-Hill
1948
|
| Edition: | 1. edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 370 Seiten Illustrationen 21 cm |
Staff View
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Record in the Search Index
| _version_ | 1804118059103813632 |
|---|---|
| adam_text | CONTENTS
Preface v
Chapter 1. Counting and Recording of Numbers
1. Numbers and counting 1
2. Basic number groups 1
3. The number systems 2
4. Large numbers 4
5. Finger numbers 5
6. Recordings of numbers 6
7. Writing of numbers 8
8. Calculations 14
9. Positional numeral systems 16
10. Hindu Arabic numerals 19
Chapter 8. Properties of Numbers. Division
1. Number theory and numerology 25
2. Multiples and divisors 28
3. Division and remainders 30
4. Number systems 34 /
5. Binary number systems 37
Chapter S. Euclid s Algorism
1. Greatest common divisor. Euclid s algorism 41
2. The division lemma 44
3. Least common multiple 45
4. Greatest common divisor and least common multiple for several
numbers 47
Chapter 4 Prime Numbers
1. Prime numbers and the prime factorization theorem 50
2. Determination of prime factors 52
vii
viii CONTENTS
3. Factor tables 53
4. Fermat s factorization method 54
5. Euler s factorization method 59
6. The sieve of Eratosthenes 64
7. Mersenne and Fermat primes 69
8. The distribution of primes 75
Chapter 5. The Aliquot Parts
1. The divisors of a number 88
2. Perfect numbers 91
3. Amicable numbers 96
4. Greatest common divisor and least common multiple 100
5. Euler s function 109
Chapter 6. Indeterminate Problems
1. Problems and puzzles 116
2. Indeterminate problems 120
3. Problems with two unknowns 124
4. Problems with several unknowns 131
Chapter 7. Theory of Linear Indeterminate Problems
1. Theory of linear indeterminate equations with two unknowns ... 142
2. Linear indeterminate equations in several unknowns 153
3. Classification of systems of numbers 158
Chapter 8. Diophantine Problems
1. The Pythagorean triangle 165
2. The Plimpton Library tablet 170
3. Diophantos of Alexandria 179
4. Al Karkhi and Leonardo Pisano 185
5. From Diophantos to Fermat 194
6. The method of infinite descent 199
7. Fermat s last theorem 203
CONTENTS ix
Chapter 9. Congruences
1. The Disquisitiones arithmeticae 209
2. The properties of congruences 211
3. Residue systems 213
4. Operations with congruences 216
5. Casting out nines 225
Chapter 10. Analysis of Congruences
1. Algebraic congruences 234
2. Linear congruences 236
3. Simultaneous congruences and the Chinese remainder theorem . . 240
4. Further study of algebraic congruences 249
Chapter 11. Wilson s Theorem and Its Consequences
1. Wilson s theorem 259
2. Gauss s generalization of Wilson s theorem 263
3. Representations of numbers as the sum of two squares 267
Chapter IS. Euler s Theorem and Its Consequences
1. Euler s theorem 272
2. Fermat s theorem 277
3. Exponents of numbers 279
4. Primitive roote for primes 284
5. Primitive roots for powers of primes 285
6. Universal exponents 290
7. Indices 294
8. Number theory and the splicing of telephone cables 302
Chapter IS. Theory of Decimal Expansions
1. Decimal fractions 311
2. The properties of decimal fractions 315
Chapter H. The Converse of Fermat s Theorem
1. The converse of Fermat s theorem 326
2. Numbers with the Fermat property 331
X CONTENTS
Chapter 15. The Classical Construction Problems
1. The classical construction problems 340
2. The construction of regular polygons 346
3. Examples of constructive polygons 352
Supplement 359
Bibliography 359d
General Name Index 361
Subject Index 365
|
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| spelling | Ore, Oystein Verfasser aut Number theory and its history by Oystein Ore 1. edition New York, NY [u.a.] McGraw-Hill 1948 X, 370 Seiten Illustrationen 21 cm txt rdacontent n rdamedia nc rdacarrier Geschichte gnd rswk-swf Geschichte Mathematik Mathematics History Number theory Geschichte (DE-588)4020517-4 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s Geschichte (DE-588)4020517-4 s 1\p DE-604 Geschichte z 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002364222&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ore, Oystein Number theory and its history Geschichte Mathematik Mathematics History Number theory Geschichte (DE-588)4020517-4 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4020517-4 (DE-588)4067277-3 |
| title | Number theory and its history |
| title_auth | Number theory and its history |
| title_exact_search | Number theory and its history |
| title_full | Number theory and its history by Oystein Ore |
| title_fullStr | Number theory and its history by Oystein Ore |
| title_full_unstemmed | Number theory and its history by Oystein Ore |
| title_short | Number theory and its history |
| title_sort | number theory and its history |
| topic | Geschichte Mathematik Mathematics History Number theory Geschichte (DE-588)4020517-4 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Geschichte Mathematik Mathematics History Number theory Zahlentheorie |
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