Higher arithmetic: an algorithmic introduction to number theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2008]
|
| Schriftenreihe: | Student mathematical library
volume 45 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 210 Seiten |
| ISBN: | 9780821844397 |
Internformat
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| 245 | 1 | 0 | |a Higher arithmetic |b an algorithmic introduction to number theory |c Harold M. Edwards |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2008] | |
| 264 | 4 | |c © 2008 | |
| 300 | |a xii, 210 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Student mathematical library |v volume 45 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface
ix
Chapter
1.
Numbers
1
Chapter
2.
The Problem
ΑΏ
+
В
=
D
7
Chapter
3.
Congruences
11
Chapter
4.
Double Congruences and the Euclidean Algorithm
17
Chapter
5.
The Augmented Euclidean Algorithm
23
Chapter
6.
Simultaneous Congruences
29
Chapter
7.
The Fundamental Theorem of Arithmetic
33
Chapter
8.
Exponentiation and Orders
37
Chapter
9.
Euler s (^-Function
43
Chapter
10.
Finding the Order of
α
mod
с
45
Chapter
11.
Primality Testing
51
vi
Higher
Arithmetic
Chapter
12.
The RSA Cipher System
57
Chapter
13.
Primitive Roots mod
ρ
61
Chapter
14.
Polynomials
67
Chapter
15.
Tables of Indices mod
ρ
71
Chapter
16.
Brahmagupta s Formula and Hypernumbers
77
Chapter
17.
Modules of Hypernumbers
81
Chapter
18.
A Canonical Form for Modules of Hypernumbers
87
Chapter
19.
Solution
οΐΑΠ + Β = Π
93
Chapter
20.
Proof of the Theorem of Chapter
19 99
Chapter
21.
Euler s Remarkable Discovery
113
Chapter
22.
Stable Modules
119
Chapter
23.
Equivalence of Modules
123
Chapter
24.
Signatures of Equivalence Classes
129
Chapter
25.
The Main Theorem
135
Chapter
26.
Modules That Become Principal When Squared
137
Chapter
27.
The Possible Signatures for Certain Values of A
143
Chapter
28.
The Law of Quadratic Reciprocity
149
Chapter
29.
Proof of the Main Theorem
153
Chapter
30.
The Theory of Binary Quadratic Forms
155
Chapter
31.
Composition of Binary Quadratic Forms
163
Contents
vii
Appendix.
Cycles
of Stable Modules
169
Answers to Exercises
179
Bibliography
207
Index
209
|
| adam_txt |
Contents
Preface
ix
Chapter
1.
Numbers
1
Chapter
2.
The Problem
ΑΏ
+
В
=
D
7
Chapter
3.
Congruences
11
Chapter
4.
Double Congruences and the Euclidean Algorithm
17
Chapter
5.
The Augmented Euclidean Algorithm
23
Chapter
6.
Simultaneous Congruences
29
Chapter
7.
The Fundamental Theorem of Arithmetic
33
Chapter
8.
Exponentiation and Orders
37
Chapter
9.
Euler's (^-Function
43
Chapter
10.
Finding the Order of
α
mod
с
45
Chapter
11.
Primality Testing
51
vi
Higher
Arithmetic
Chapter
12.
The RSA Cipher System
57
Chapter
13.
Primitive Roots mod
ρ
61
Chapter
14.
Polynomials
67
Chapter
15.
Tables of Indices mod
ρ
71
Chapter
16.
Brahmagupta's Formula and Hypernumbers
77
Chapter
17.
Modules of Hypernumbers
81
Chapter
18.
A Canonical Form for Modules of Hypernumbers
87
Chapter
19.
Solution
οΐΑΠ + Β = Π
93
Chapter
20.
Proof of the Theorem of Chapter
19 99
Chapter
21.
Euler's Remarkable Discovery
113
Chapter
22.
Stable Modules
119
Chapter
23.
Equivalence of Modules
123
Chapter
24.
Signatures of Equivalence Classes
129
Chapter
25.
The Main Theorem
135
Chapter
26.
Modules That Become Principal When Squared
137
Chapter
27.
The Possible Signatures for Certain Values of A
143
Chapter
28.
The Law of Quadratic Reciprocity
149
Chapter
29.
Proof of the Main Theorem
153
Chapter
30.
The Theory of Binary Quadratic Forms
155
Chapter
31.
Composition of Binary Quadratic Forms
163
Contents
vii
Appendix.
Cycles
of Stable Modules
169
Answers to Exercises
179
Bibliography
207
Index
209 |
| any_adam_object | 1 |
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| author | Edwards, Harold M. 1936-2020 |
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| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)181072698 (DE-599)BVBBV023304212 |
| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T20:47:49Z |
| indexdate | 2024-07-09T21:15:25Z |
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| isbn | 9780821844397 |
| language | English |
| lccn | 2007060578 |
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| physical | xii, 210 Seiten |
| publishDate | 2008 |
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| series | Student mathematical library |
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| spelling | Edwards, Harold M. 1936-2020 Verfasser (DE-588)117709700 aut Higher arithmetic an algorithmic introduction to number theory Harold M. Edwards Providence, Rhode Island American Mathematical Society [2008] © 2008 xii, 210 Seiten txt rdacontent n rdamedia nc rdacarrier Student mathematical library volume 45 Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2153-3 Student mathematical library volume 45 (DE-604)BV013184751 45 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016488611&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Edwards, Harold M. 1936-2020 Higher arithmetic an algorithmic introduction to number theory Student mathematical library Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 |
| title | Higher arithmetic an algorithmic introduction to number theory |
| title_auth | Higher arithmetic an algorithmic introduction to number theory |
| title_exact_search | Higher arithmetic an algorithmic introduction to number theory |
| title_exact_search_txtP | Higher arithmetic an algorithmic introduction to number theory |
| title_full | Higher arithmetic an algorithmic introduction to number theory Harold M. Edwards |
| title_fullStr | Higher arithmetic an algorithmic introduction to number theory Harold M. Edwards |
| title_full_unstemmed | Higher arithmetic an algorithmic introduction to number theory Harold M. Edwards |
| title_short | Higher arithmetic |
| title_sort | higher arithmetic an algorithmic introduction to number theory |
| title_sub | an algorithmic introduction to number theory |
| topic | Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Number theory Zahlentheorie |
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