Fundamental number theory with applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2008
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Discrete mathematics and its applications
47 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 351-354) and index |
| Beschreibung: | X, 369 S. |
| ISBN: | 9781420066593 1420066595 |
Internformat
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| 100 | 1 | |a Mollin, Richard A. |d 1947- |e Verfasser |0 (DE-588)124930859 |4 aut | |
| 245 | 1 | 0 | |a Fundamental number theory with applications |c Richard A. Mollin |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2008 | |
| 300 | |a X, 369 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Discrete mathematics and its applications |v 47 | |
| 500 | |a Includes bibliographical references (p. 351-354) and index | ||
| 650 | 4 | |a Number theory | |
| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804137662980816896 |
|---|---|
| adam_text | Contents
Preface
.
їх
Arithmetic of the Integers
1
1.1
Induction
.............................. 1
1.2
Division
............................... 16
1.3
Primes
................................ 30
1.4
The Chinese Remainder Theorem
............... 40
1.5
Thue s Theorem
.......................... 44
1.6
Combinatorial Number Theory
................ 49
1.7
Partitions and Generating Functions
............. 55
1.8
True Primality Tests
....................... 60
1.9
Distribution of Primes
...................... 65
Modular Arithmetic
73
2.1
Basic Properties
.......................... 73
2.2
Modular Perspective
....................... 84
2.3
Arithmetic Functions:
Euler,
Carmichael, and
Möbius
. . 90
2.4
Number and Sums of Divisors
.................102
2.5
The Floor and the Ceiling
....................108
2.6
Polynomial Congruences
.....................113
2.7
Primality Testing
.........................119
2.8
Cryptology
.............................127
Primitive Roots
139
3.1
Order
.................................139
3.2
Existence
..............................145
3.3
Indices
................................153
3.4
Random Number Generation
..................160
3.5
Public-Key Cryptography
....................166
Quadratic Residues
177
4.1
The Legendre Symbol
......................177
4.2
The Quadratic Reciprocity Law
................189
4.3
Factoring
...............................201
VII
Vlil
5
Simple
Continued Fractions and Diophantine Approximation
209
5.1
Infinite Simple Continued Fractions
............. 209
5.2
Periodic Simple Continued Fractions
............. 221
5.3
Pell s Equation and Surds
.................... 232
5.4
Continued Fractions and Factoring
.............. 240
6
Additivity
—
Sums of Powers
243
6.1
Sums of Two Squares
....................... 243
6.2
Sums of Three Squares
...................... 252
6.3
Sums of Four Squares
...................... 254
6.4
Sums of Cubes
........................... 259
7
Diophantine Equations
265
7.1
Norm-Form Equations
...................... 265
7.2
The Equation ax2
+
by2
+
cz2
= 0 ............... 274
7.3
Bachet s Equation
......................... 277
7.4
Fermat s Last Theorem
..................... 281
Appendix A: Fundamental Facts
.............................285
Appendix B: Complexity
....................................311
Appendix C: Primes
< 9547
and Least Primitive Roots
......313
Appendix
Đ:
Indices
.........................................318
Appendix E: The ABC Conjecture
...........................319
Appendix F: Primes is in
Ρ
..................................320
Solutions to Odd-Numbered Exercises
.......................323
Bibliography
................................................351
List of Symbols
..............................................355
Index
........................................................356
About the Author
...........................................369
|
| adam_txt |
Contents
Preface
.
їх
Arithmetic of the Integers
1
1.1
Induction
. 1
1.2
Division
. 16
1.3
Primes
. 30
1.4
The Chinese Remainder Theorem
. 40
1.5
Thue's Theorem
. 44
1.6
Combinatorial Number Theory
. 49
1.7
Partitions and Generating Functions
. 55
1.8
True Primality Tests
. 60
1.9
Distribution of Primes
. 65
Modular Arithmetic
73
2.1
Basic Properties
. 73
2.2
Modular Perspective
. 84
2.3
Arithmetic Functions:
Euler,
Carmichael, and
Möbius
. . 90
2.4
Number and Sums of Divisors
.102
2.5
The Floor and the Ceiling
.108
2.6
Polynomial Congruences
.113
2.7
Primality Testing
.119
2.8
Cryptology
.127
Primitive Roots
139
3.1
Order
.139
3.2
Existence
.145
3.3
Indices
.153
3.4
Random Number Generation
.160
3.5
Public-Key Cryptography
.166
Quadratic Residues
177
4.1
The Legendre Symbol
.177
4.2
The Quadratic Reciprocity Law
.189
4.3
Factoring
.201
VII
Vlil
5
Simple
Continued Fractions and Diophantine Approximation
209
5.1
Infinite Simple Continued Fractions
. 209
5.2
Periodic Simple Continued Fractions
. 221
5.3
Pell's Equation and Surds
. 232
5.4
Continued Fractions and Factoring
. 240
6
Additivity
—
Sums of Powers
243
6.1
Sums of Two Squares
. 243
6.2
Sums of Three Squares
. 252
6.3
Sums of Four Squares
. 254
6.4
Sums of Cubes
. 259
7
Diophantine Equations
265
7.1
Norm-Form Equations
. 265
7.2
The Equation ax2
+
by2
+
cz2
= 0 . 274
7.3
Bachet's Equation
. 277
7.4
Fermat's Last Theorem
. 281
Appendix A: Fundamental Facts
.285
Appendix B: Complexity
.311
Appendix C: Primes
< 9547
and Least Primitive Roots
.313
Appendix
Đ:
Indices
.318
Appendix E: The ABC Conjecture
.319
Appendix F: Primes is in
Ρ
.320
Solutions to Odd-Numbered Exercises
.323
Bibliography
.351
List of Symbols
.355
Index
.356
About the Author
.369 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
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| illustrated | Not Illustrated |
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| isbn | 9781420066593 1420066595 |
| language | English |
| lccn | 2007050650 |
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| series | Discrete mathematics and its applications |
| series2 | Discrete mathematics and its applications |
| spelling | Mollin, Richard A. 1947- Verfasser (DE-588)124930859 aut Fundamental number theory with applications Richard A. Mollin 2. ed. Boca Raton [u.a.] Chapman & Hall/CRC 2008 X, 369 S. txt rdacontent n rdamedia nc rdacarrier Discrete mathematics and its applications 47 Includes bibliographical references (p. 351-354) and index Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s DE-604 Discrete mathematics and its applications 47 (DE-604)BV023551867 47 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016507281&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mollin, Richard A. 1947- Fundamental number theory with applications Discrete mathematics and its applications Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 |
| title | Fundamental number theory with applications |
| title_auth | Fundamental number theory with applications |
| title_exact_search | Fundamental number theory with applications |
| title_exact_search_txtP | Fundamental number theory with applications |
| title_full | Fundamental number theory with applications Richard A. Mollin |
| title_fullStr | Fundamental number theory with applications Richard A. Mollin |
| title_full_unstemmed | Fundamental number theory with applications Richard A. Mollin |
| title_short | Fundamental number theory with applications |
| title_sort | fundamental number theory with applications |
| topic | Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Number theory Zahlentheorie |
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