A cascade of numbers: an introduction to number theory
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London u.a.
Arnold
1996
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 148 S. |
| ISBN: | 0340652519 |
Staff View
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Record in the Search Index
| _version_ | 1804125028140187648 |
|---|---|
| adam_text | Contents
Comments
and
Solutions
Preface vii
Definitions ix
Part I 1 75
1. The magic of nines (decimal place value) 3 77
2. Back to basics (bicimal place value) 5 78
3. Children s ages (prime factorisation part i) 5 79
4. The prison door problem (counting factors) 5 79
5. Catching practice (repeated addition around a circle part i) 7 81
6. Algorithma (highest common factor, part i) 8 81
7. Breeding rabbits (Fibonacci, using factors) 10 82
8. To divide or not to divide (prime factorisation part ii) 12 83
9. A return visit to Algorithma (highest common factor, part ii,
the fundamental theorem of arithmetic) 13 84
10. The stamp problem 13 85
11. Tests for divisibility (decimal place value) 15 86
12. Spot check (first taste of modulo 10) 15
13. Eratosthenes sieve (locating primes, proof by contradiction) 17 87
14. Raffle tickets and neighbours (primes and composites) 17 88
15. How many primes? (no finite number, contradiction again) 18 88
16. No shuffling (first taste of modulo 4) 19 89
17. Can you really tell the time? (modulo 12 and modulo 4) 19 90
18. Fibonacci numbers and the division algorithm 21 92
19. Relations can be difficult (equivalence) 22 93
20. Dominoes (induction) 25 95
Part II 29 99
21. Chinese remainders 31 101
22. Systematic catching practice (repeated addition part ii, 0) 32 102
23. Do you know your tables? (modular multiplication) 33 104
24. Coding and decoding (simple methods) 34 107
25. Repacking (squares and their residues) 35 107
26. Where have all the squares gone? 36 108
27. Where have all the squares come from? 36 109
28. How old is Grandma? (applying quadratic residues) 37 110
29. Higher powers (approaching Fermat s theorem) 39 111
30. Just shuffling and then pow (modulo 7) (Fermat s theorem
parti) 40 112
31. Just shuffling and then paKa (modulo 3, 5, 11) (Fermat s
theorem part ii) 41 113
vi Contents
Comments
and
Solutions
32. Factorials (Wilson s theorem) 43 114
33. Square roots of 1, prime modulus (p*= 1, 3 (mod4)) 43 115
34. How many square roots of 1? (factors of x + 1) 44 115
35. Sums of squares 44 116
36. Sums of squares in two ways 46 117
37. Pythagorean triples 47 118
Part HI 49 121
38. Squares and non squares (quadratic residues and products) 51 123
39. Powers of squares and non squares (towards the Legendre
symbol) 52 123
40. The frequency of factors (Ltyd)) 52 124
41. Multiplication like addition (cyclic groups and generators) 53 125
42. Powers to a prime modulus (primitive roots) 54 126
43. Zero products (modulo a non prime) 56 127
44. Non zero products (Fermat Euler theorem) 57 128
45. Decimals to the death (recurring decimals to fractions) 57 129
46. Recurring decimals (fractions to recurring decimals) 58 131
47. Can you reveal all and keep it secret? (Public Key System) 60 133
48. Primes as squares and non squares (starting quadratic
reciprocity) 62 134
49. Counting dots in a rectangle (odd or even) 64 135
50. Half size products (Gauss lemma, when 2 is a square) 64 136
51. From dashes to dots (Eisenstein) 66 138
52. Quadratic reciprocity 68 141
53. Adding squares (primes in various forms) 70 143
Index 147
|
| any_adam_object | 1 |
| author | Burn, Robert P. Chetwynd, Amanda |
| author_facet | Burn, Robert P. Chetwynd, Amanda |
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| author_sort | Burn, Robert P. |
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| dewey-full | 512.7 |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010558540 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:55:02Z |
| institution | BVB |
| isbn | 0340652519 |
| language | English |
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| physical | VIII, 148 S. |
| publishDate | 1996 |
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| publisher | Arnold |
| record_format | marc |
| spelling | Burn, Robert P. Verfasser aut A cascade of numbers an introduction to number theory arranged by Bob Burn ; Amanda Chetwynd London u.a. Arnold 1996 VIII, 148 S. txt rdacontent n rdamedia nc rdacarrier Number theory Problems, exercises, etc Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s DE-604 Chetwynd, Amanda Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007039012&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Burn, Robert P. Chetwynd, Amanda A cascade of numbers an introduction to number theory Number theory Problems, exercises, etc Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 |
| title | A cascade of numbers an introduction to number theory |
| title_auth | A cascade of numbers an introduction to number theory |
| title_exact_search | A cascade of numbers an introduction to number theory |
| title_full | A cascade of numbers an introduction to number theory arranged by Bob Burn ; Amanda Chetwynd |
| title_fullStr | A cascade of numbers an introduction to number theory arranged by Bob Burn ; Amanda Chetwynd |
| title_full_unstemmed | A cascade of numbers an introduction to number theory arranged by Bob Burn ; Amanda Chetwynd |
| title_short | A cascade of numbers |
| title_sort | a cascade of numbers an introduction to number theory |
| title_sub | an introduction to number theory |
| topic | Number theory Problems, exercises, etc Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Number theory Problems, exercises, etc Zahlentheorie |
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