An introduction to the theory of numbers:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1980
|
| Ausgabe: | 4. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 335 S. |
| ISBN: | 0471028517 |
Internformat
MARC
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| 245 | 1 | 0 | |a An introduction to the theory of numbers |c Ivan Niven ; Herbert S. Zuckerman |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1980 | |
| 300 | |a XII, 335 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Nombres, Théorie des | |
| 650 | 4 | |a Number theory | |
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Datensatz im Suchindex
| _version_ | 1804116739675389952 |
|---|---|
| adam_text | Contents
1. Divisibility
1.1 Introduction... 1
1.2 Divisibility...4
1.3 Primes...l7
2. Congruences
2.1 Congruences...29
2.2 Solutions of Congruences...39
2.3 An Algorithm for Linear Congruences, and the
Chinese Remainder Theorem...41
2.4 The Function K«). 48
2.5 Congruences of Higher Degree...51
2.6 Prime Power Moduli...53
2.7 Prime Modulus...56
2.8 Congruences of Degree Two, Prime Modulus...61
2.9 Power Residues...61
2.10 Number Theory from an Algebraic Viewpoint...67
2.11 Multiplicative Groups, Rings, and Fields...72
2.12 The Multiplicative Group Modulo /W...78
3. Quadratic Reciprocity
3.1 Quadratic Residues...85
3.2 Quadratic Reciprocity...90
3.3 The Jacobi Symbol...93
3.4 On Algorithms and Computing...98
4. Some Functions of Number Theory
4.1 Greatest Integer Function... 100
4.2 Arithmetic Functions... 107
x Contents
4.3 The Moebius Inversion Fonnula...lll
4.4 The Multiplication of Arithmetic Functions... 114
4.5 Recurrence Functions... 121
4.6 Combinatorial Number Theory... 124
5. Some Diophantine Equations
5.1 Diophantine Equations...130
5.2 The Equation ax + by = c... 130
5.3 Positive Solutions... 133
5.4 Other Linear Equations...135
5.5 The Equation x2+y2 = z2...138
5.6 The Equation x4+y4 = z2...l39
5.7 Sums of Four and Five Squares... 142
5.8 Waring s Problem... 146
5.9 Sum of Fourth Powers... 146
5.10 Sum of Two Squares... 147
5.11 The Equation 4x2+y2=n... 152
5.12 The Equation ax2+by2 + cz2 = 0...l55
5.13 Binary Quadratic Forms...l58
5.14 Equivalence of Quadratic Forms... 162
6. Farey Fractions and Irrational Numbers
6.1 Farey Sequences... 170
6.2 Rational Approximations... 173
6.3 Irrational Numbers... 179
6.4 Coverings of the Real Line... 183
7. Simple Continued Fractions
7.1 The Euclidean Algorithm... 186
7.2 Uniqueness... 188
7.3 Infinite Continued Fractions... 190
7.4 Irrational Numbers... 194
7.5 Approximations to Irrational Numbers... 196
7.6 Best Possible Approximations...201
7.7 Periodic Continued Fractions...204
7.8 Pell s Equation...209
7.9 Numerical Computation...215
8. Elementary Remarks on the Distribution of Primes
8.1 The Function w(x)...217
Contents
8.2 The Sequence of Primes...22O
8.3 Bertrand s Postulate... 224
8.4 Primes in Special Arithmetic Progressions...226
9. Algebraic Numbers
9.1 Polynomials...231
9.2 Algebraic Numbers...235
9.3 Algebraic Number Fields...24O
9.4 Algebraic Integers...245
9.5 Quadratic Fields...246
9.6 Units in Quadratic Fields...249
9.7 Primes in Quadratic Fields...25O
9.8 Unique Factorization...252
9.9 Primes in Quadratic Fields Having the Unique
Factorization Property...254
9.10 The Equation x3 + y3 = z3...261
10. The Partition Function
10.1 Partitions...267
10.2 Graphs...268
10.3 Formal Power Series and Euler s Identity...271
10.4 Euler s Formula...275
10.5 Jacobi s Formula...281
10.6 A Divisibility Property...284
11. The Density of Sequences of Integers
11.1 Asymptotic Density...289
11.2 Square Free Integers...292
11.3 Sets of Density Zero...295
11.4 Schnirelmann Density and the afi Theorem...299
Special Topics..305
Periodic decimals, Unit fractions, The equation x +
y~ = z~ , Gauss s generalization of Fermat s theorem,
Primitive root mod p by group theory, The group of
rational points on the unit circle, The day of the week
from the date, Some number theoretic determinants,
Gaussian integers as sums of squares, Unique factoriza¬
tion in Gaussian integers, The Eisenstein irreducibility
criterion.
xii Contents
Prime Numbers Less Than 2000..317
General References..318
Answers to Problems..320
Index..331
|
| any_adam_object | 1 |
| author | Niven, Ivan 1915-1999 Zuckerman, Herbert S. -1970 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)5726666 (DE-599)BVBBV002280938 |
| 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 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 4. ed. |
| format | Book |
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| institution | BVB |
| isbn | 0471028517 |
| language | English |
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| physical | XII, 335 S. |
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| publishDate | 1980 |
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| spelling | Niven, Ivan 1915-1999 Verfasser (DE-588)115101217 aut An introduction to the theory of numbers Ivan Niven ; Herbert S. Zuckerman 4. ed. New York [u.a.] Wiley 1980 XII, 335 S. txt rdacontent n rdamedia nc rdacarrier Nombres, Théorie des Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Zahlentheorie (DE-588)4067277-3 s DE-604 Zuckerman, Herbert S. -1970 Verfasser (DE-588)115101225 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001498856&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Niven, Ivan 1915-1999 Zuckerman, Herbert S. -1970 An introduction to the theory of numbers Nombres, Théorie des Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4151278-9 |
| title | An introduction to the theory of numbers |
| title_auth | An introduction to the theory of numbers |
| title_exact_search | An introduction to the theory of numbers |
| title_full | An introduction to the theory of numbers Ivan Niven ; Herbert S. Zuckerman |
| title_fullStr | An introduction to the theory of numbers Ivan Niven ; Herbert S. Zuckerman |
| title_full_unstemmed | An introduction to the theory of numbers Ivan Niven ; Herbert S. Zuckerman |
| title_short | An introduction to the theory of numbers |
| title_sort | an introduction to the theory of numbers |
| topic | Nombres, Théorie des Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Nombres, Théorie des Number theory Zahlentheorie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001498856&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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