An introduction to the theory of numbers:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1972
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 288 S. |
Internformat
MARC
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| 100 | 1 | |a Niven, Ivan |d 1915-1999 |e Verfasser |0 (DE-588)115101217 |4 aut | |
| 245 | 1 | 0 | |a An introduction to the theory of numbers |c Ivan Niven ; Herbert S. Zuckerman |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1972 | |
| 300 | |a XII, 288 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Nombres, Théorie des | |
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Datensatz im Suchindex
| _version_ | 1804118057118859264 |
|---|---|
| adam_text | Contents
1. Divisibility 1
1.1 Introduction 1
1.2 Divisibility 2
1.3 Primes 10
2. Congruences 20
2.1 Congruences 20
2.2 Solutions of Congruences 27
2.3 Congruences of Degree I 29
2.4 The Function f (n) 34
2.5 Congruences of Higher Degree 37
2.6 Prime Power Moduli 39
2.7 Prime Modulus 43
2.8 Congruences of Degree Two, Prime Modulus 46
2.9 Power Residues 46
2.10 Number Theory from an Algebraic Viewpoint 51
2.11 Multiplicative Groups, Rings, and Fields 56
3. Quadratic Reciprocity 63
3.1 Quadratic Residues 63
3.2 Quadratic Reciprocity 67
3.3 The Jacobi Symbol 71
4. Some Functions of Number Theory 78
4.1 Greatest Integer Function 78
4.2 Arithmetic Functions 84
4.3 The Moebius Inversion Formula 88
ix
x Contents
4.4 The Multiplication of Arithmetic Functions 91
4.5 Recurrence Functions 96
5. Some Diophantine Equations 100
5.1 Diophantine Equations 100
5.2 The Equation ax + by = c 101
5.3 Positive Solutions 102
5.4 Other Linear Equations 104
5.5 The Equation x2 + y2 = z2 105
5.6 The Equation x4 + f = z2 107
5.7 Sums of Four and Five Squares 109
5.8 Waring s Problem 112
5.9 Sum of Fourth Powers 112
5.10 Sum of Two Squares 113
5.11 The Equation 4x2 + f = n 118
5.12 The Equation ox2 + bf + cz2 = 0 120
5.13 Binary Quadratic Forms 123
5.14 Equivalence of Quadratic Forms 127
6. Farey Fractions and Irrational Numbers 134
6.1 Farey Sequences 134
6.2 Rational Approximations 137
6.3 Irrational Numbers 142
6.4 Coverings of the Real Line 147
7. Simple Continued Fractions 150
7.1 The Euclidean Algorithm 150
7.2 Uniqueness 152
7.3 Infinite Continued Fractions 153
7.4 Irrational Numbers 157
7.5 Approximations to Irrational Numbers 159
7.6 Best Possible Approximations 163
7.7 Periodic Continued Fractions 166
7.8 Pell s Equation 172
7.9 Numerical Computation 175
Contents xi
8. Elementary Remarks on the Distribution of Primes 178
8.1 The Function n(x) 178
8.2 The Sequence of Primes 181
8.3 Bertrand s Postulate 185
9. Algebraic Numbers 188
9.1 Polynomials 188
9.2 Algebraic Numbers 192
9.3 Algebraic Number Fields 195
9.4 Algebraic Integers 199
9.5 Quadratic Fields 201
9.6 Units in Quadratic Fields 203
9.7 Primes in Quadratic Fields 204
9.8 Unique Factorization 206
9.9 Primes in Quadratic Fields Having the Unique
Factorization Property 208
9.10 The Equation x3 + f = z3 213
10. The Partition Function 219
10.1 Partitions 219
10.2 Graphs 220
10.3 Formal Power Series and Euler s Identity 223
10.4 Euler s Formula 227
10.5 Jacobi s Formula 233
10.6 A Divisibility Property 236
11. The Density of Sequences of Integers 240
11.1 Asymptotic Density 241
11.2 Square-Free Integers 243
11.3 Sets of Density Zero 246
11.4 Schnirelmann Density and the at.fi Theorem 250
xii Contents
Miscellaneous Problems 255
Special Topics 259
Periodic decimals, Unit fractions, The equation
x~n + y~n = z~n. 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 factorization in Gaussian integers, The
Eisenstein irreducibility criterion.
General References 269
Answers to Problems 271
Index 285
|
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512/.7 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| language | English |
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| physical | XII, 288 S. |
| publishDate | 1972 |
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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 3. ed. New York [u.a.] Wiley 1972 XII, 288 S. txt rdacontent n rdamedia nc rdacarrier Nombres, Théorie des Numbers, Theory of 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=002362864&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 Numbers, Theory of 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 Numbers, Theory of Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Nombres, Théorie des Numbers, Theory of Number theory Zahlentheorie Einführung |
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