Discovering number theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia, Pa.
Saunders
1972
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 129 Seiten Ill., graph. Darst. |
| ISBN: | 0721661866 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804121414629851136 |
|---|---|
| adam_text | Contents
CHAPTER 1
The Integers 1
1.1 Discussion of the Counting Numbers 2
1.2 Arithmetic 3
Suggested Project 5
CHAPTER 2
Divisors 8
2.1 Division 9
2.2 Greatest Common Divisor 13
2.3 The Ideal (a,b) 19
Suggested Projects 20
CHAPTER 3
Primes 21
3.1 Relatively Prime Integers and Prime Integers 21
3.2 The Sieve of Eratosthenes 24
Suggested Projects 26
CHAPTER 4
Unique Factorization 27
4.1 The Fundamental Theorem of Arithmetic 27
4.2 GCD and LCM of Factored Integers 28
vii
CHAPTER 5
Congruences 32
5.1 Clock Arithmetic, a Kind of Equivalence 32
5.2 Equivalence Classes and Their Representatives 36
5.3 Divisibility of Large Numbers 41
Suggested Projects 44
CHAPTER 6
Solving Congruences 45
6.1 Linear Congruences 46
6.2 Simultaneous Linear Congruences 50
Suggested Project 53
CHAPTER 7
Elements Prime to the Modulus 55
7.1 The Euler Phi Function 55
7.2 Exponentiation 58
7.3 Binomial Coefficients 58
7.4 Fermat s Theorem and Euler s Theorem 60
Suggested Project 63
CHAPTER 8
Primitive Roots and Indices 64
8.1 Order of an Element 64
8.2 Indices 66
8.3 Power Residues 69
8.4 Higher Degree Congruences 70
Suggested Project 70
CHAPTER 9
Diophantine Problems .71
9.1 Linear Problems 71
9.2 Pythagorean Triples 74
9.3 Difference of Two Squares 76
9.4 The Four Square Theorem 77
9.5 Waring s Problem 79
Suggested Projects 79
viii
CHAPTER 10
Fibonacci Numbers so
10.1 The Fibonacci Sequence 80
10.2 The Golden Section 82
10.3 Divisibility 82
10.4 Completeness 86
10.5 Approximation Using Fibonacci Numbers 88
Suggested Projects 90
CHAPTER 11
Pell s Equation 92
Suggested Project 94
CHAPTER 12
Magic Numbers 95
12.1 Perfect Numbers 95
12.2 Amicable Numbers 101
12.3 Magic Squares 102
Suggested Projects 104
CHAPTER 13
Figures with Shapes 105
13.1 /n Gonal Numbers 106
13.2 Pyramidal Numbers 110
13.3 Pascal s Triangle 111
Suggested Project 111
CHAPTER 14
Inside Integers 112
14.1 The Mobius Function 112
14.2 The Mobius Inversion Formula 115
CHAPTER 15
Fermat s Last Theorem 119
Answers to Selected Exercises 121
Index 127
ix
|
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| id | DE-604.BV007204582 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:57:36Z |
| institution | BVB |
| isbn | 0721661866 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004611484 |
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| physical | IX, 129 Seiten Ill., graph. Darst. |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Saunders |
| record_format | marc |
| spelling | Maxfield, John Edward Verfasser aut Discovering number theory John E. Maxfield and Margaret W. Maxfield Philadelphia, Pa. Saunders 1972 IX, 129 Seiten Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s DE-604 Maxfield, Margaret W. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004611484&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Maxfield, John Edward Maxfield, Margaret W. Discovering number theory Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 |
| title | Discovering number theory |
| title_auth | Discovering number theory |
| title_exact_search | Discovering number theory |
| title_full | Discovering number theory John E. Maxfield and Margaret W. Maxfield |
| title_fullStr | Discovering number theory John E. Maxfield and Margaret W. Maxfield |
| title_full_unstemmed | Discovering number theory John E. Maxfield and Margaret W. Maxfield |
| title_short | Discovering number theory |
| title_sort | discovering number theory |
| topic | Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Number theory Zahlentheorie |
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