Problem-solving and selected topics in number theory: in the spirit of the mathematical olympiads
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
2011
|
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-1-4419-0494-2 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021117942&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIII, 324 S. graph. Darst. |
| ISBN: | 9781441904942 |
| DOI: | 10.1007/978-1-4419-0494-2 |
Internformat
MARC
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| 100 | 1 | |a Rassias, Michael Th. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Problem-solving and selected topics in number theory |b in the spirit of the mathematical olympiads |c Michael Th. Rassias |
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2011 | |
| 300 | |a XIII, 324 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021117942&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-021117942 | |
Datensatz im Suchindex
| _version_ | 1819349675396825088 |
|---|---|
| adam_text | Contents
Foreword by
Preda Mihăilescu
................................. ix
Acknowledgments
............................................. xv
1
Introduction
............................................... 1
1.1
Basic notions
........................................... 1
1.2
Basic methods to compute the greatest common divisor
...... 4
1.2.1
The Euclidean algorithm
........................... 5
1.2.2
Blankinship
s
method
.............................. 5
1.3
The fundamental theorem of arithmetic
.................... 6
1.4
Rational and irrational numbers
........................... 8
2
Arithmetic functions
....................................... 15
2.1
Basic definitions
......................................... 15
2.2
The
Möbius
function
..................................... 16
2.3
The
Euler
function
...................................... 20
2.4
The 7-function
.......................................... 24
2.5
The generalized a-function
................................ 26
3
Perfect numbers,
Fermat
numbers
......................... 29
3.1
Perfect numbers
......................................... 29
3.1.1
Related open problems
............................. 31
3.2
Fermat
numbers
......................................... 32
3.2.1
Some basic properties
.............................. 32
4
Congruences
............................................... 37
4.1
Basic theorems
.......................................... 37
5
Quadratic residues
......................................... 51
5.1
Introduction
............................................ 51
viii Contents
5.2
Legendre s
symbol
....................................... 56
5.2.1
The law of quadratic reciprocity
..................... 62
5.3
Jacobi s symbol
......................................... 70
5.3.1
An application of the Jacobi symbol to cryptography
. . 77
6
The
7Г-
and li-functions
.................................... 79
6.1
Basic notions and historical remarks
....................... 79
6.2
Open problems concerning prime numbers
.................. 82
7
The Riemann
zeta
function
................................ 83
7.1
Definition and RiemamYs paper
........................... 83
7.2
Some basic properties of the
Ç-function
..................... 84
7.2.1
Applications
...................................... 95
8
Dirichlet series
............................................ 99
8.1
Basic notions
........................................... 99
9
Special topics
..............................................103
9.1
The harmonic series of prime numbers
.....................103
9.2
Lagrange s four-square theorem
...........................112
9.3
Bertrand s postulate
.....................................120
9.4
An inequality for the
π
-function
...........................
129
9.5
Some diophantine equations
..............................137
9.6
Fermat
s
two-square theorem
..............................143
10
Problems
..................................................147
11
Solutions
..................................................163
12
Appendix
..................................................291
12.1
Prime number theorem
...................................291
12.2
A brief history of
Fermaťs
last theorem
....................306
12.3
Catalan s conjecture
.....................................310
References
.....................................................317
Index of Symbols
..............................................321
Index
..........................................................323
|
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| id | DE-604.BV037203751 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T14:46:34Z |
| institution | BVB |
| isbn | 9781441904942 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021117942 |
| oclc_num | 707103675 |
| open_access_boolean | |
| owner | DE-703 DE-824 DE-11 DE-188 |
| owner_facet | DE-703 DE-824 DE-11 DE-188 |
| physical | XIII, 324 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| spellingShingle | Rassias, Michael Th Problem-solving and selected topics in number theory in the spirit of the mathematical olympiads Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 |
| title | Problem-solving and selected topics in number theory in the spirit of the mathematical olympiads |
| title_auth | Problem-solving and selected topics in number theory in the spirit of the mathematical olympiads |
| title_exact_search | Problem-solving and selected topics in number theory in the spirit of the mathematical olympiads |
| title_full | Problem-solving and selected topics in number theory in the spirit of the mathematical olympiads Michael Th. Rassias |
| title_fullStr | Problem-solving and selected topics in number theory in the spirit of the mathematical olympiads Michael Th. Rassias |
| title_full_unstemmed | Problem-solving and selected topics in number theory in the spirit of the mathematical olympiads Michael Th. Rassias |
| title_short | Problem-solving and selected topics in number theory |
| title_sort | problem solving and selected topics in number theory in the spirit of the mathematical olympiads |
| title_sub | in the spirit of the mathematical olympiads |
| topic | Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Zahlentheorie |
| url | https://doi.org/10.1007/978-1-4419-0494-2 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021117942&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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