A friendly introduction to number theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston ; Munich [u.a.]
Pearson Education
[2014]
|
| Ausgabe: | 4. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes index. |
| Beschreibung: | IX, 409 S. |
| ISBN: | 9780321816191 0321816196 |
Internformat
MARC
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| 245 | 1 | 0 | |a A friendly introduction to number theory |c Joseph H. Silverman |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Boston ; Munich [u.a.] |b Pearson Education |c [2014] | |
| 300 | |a IX, 409 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes index. | ||
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Datensatz im Suchindex
| _version_ | 1804148921121898497 |
|---|---|
| adam_text | Contents
Preface
..............................................................
v
Flowchart of Chapter Dependencies
................................... ix
Introduction
......................................................... 1
1
What Is Number Theory?
............................................. 6
2
Pythagorean Triples
................................................. 13
3
Pythagorean Triples and the Unit Circle
............................... 21
4
Sums of Higher Powers and Fermat s Last Theorem
.................... 26
5
Divisibility and the Greatest Common Divisor
......................... 30
6
Linear Equations and the Greatest Common Divisor
.................... 37
7
Factorization and the Fundamental Theorem of Arithmetic
.............. 46
8
Congruences
........................................................ 55
9
Congruences, Powers, and Fermat s Little Theorem
..................... 65
10
Congruences, Powers, and Euler s Formula
............................ 71
11
Euler s Phi Function and the Chinese Remainder Theorem
.............. 75
12
Prime Numbers
..................................................... 83
13
Counting Primes
.................................................... 90
14
Mersenne Primes
.................................................... 96
15
Mersenne Primes and Perfect Numbers
............................... 101
16
Powers Modulo
m
and Successive Squaring
...........................
Ill
17
Computing k* Roots Modulo
m
..................................... 118
18
Powers, Roots, and Unbreakable Codes
............................ 123
19
Primality Testing and Carmichael Numbers
........................... 129
20
Squares Modulo/?
.................................................. 141
21
Is
-1
a Square Modulo pi Is
2?..................................... 148
22
Quadratic Reciprocity
.............................................. 159
iv CONTENTS
23
Proof of Quadratic Reciprocity
...................................... 171
24
Which Primes Are Sums of Two Squares?
............................ 181
25
Which Numbers Are Sums of Two Squares?
.......................... 193
26
As Easy as One, Two, Three
........................................ 199
27
Euler s Phi Function and Sums of Divisors
........................... 206
28
Powers Modulo
ρ
and Primitive Roots
............................... 211
29
Primitive Roots and Indices
......................................... 224
30
The Equation
XĄ+Y4=ZĄ
.......................................... 231
31
Square-Triangular Numbers Revisited
............................... 236
32
Pell s Equation
.................................................... 245
33
Diophantine Approximation
......................................... 251
34
Diophantine Approximation and Pell s Equation
...................... 260
35
Number Theory and Imaginary Numbers
............................. 267
36
The Gaussian Integers and Unique Factorization
...................... 281
37
Irrational Numbers and Transcendental Numbers
...................... 297
38
Binomial Coefficients and Pascal s Triangle
.......................... 313
39
Fibonacci s Rabbits and Linear Recurrence Sequences
................. 324
40
Oh, What a Beautiful Function
...................................... 339
41
Cubic Curves and Elliptic Curves
.................................... 353
42
Elliptic Curves with Few Rational Points
............................. 366
43
Points on Elliptic Curves Modulo
ρ
.................................. 373
44
Torsion Collections Modulo
ρ
and Bad Primes
........................ 384
45
Defect Bounds and Modularity Patterns
.............................. 388
46
Elliptic Curves and
Fermaťs
Last Theorem
........................... 394
Further Reading
................................................... 396
Index
............................................................. 397
47
The Topsy-Turvy World of Continued Fractions [online]
............... 410
48
Continued Fractions and Pell s Equation [online]
...................... 426
49
Generating Functions [online]
....................................... 442
50
Sums of Powers [online]
............................................ 452
A Factorization of Small Composite Integers [online]
.................... 464
В
A List of Primes [online]
........................................... 466
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 4. ed. |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:14:49Z |
| institution | BVB |
| isbn | 9780321816191 0321816196 |
| language | English |
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| physical | IX, 409 S. |
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| spelling | Silverman, Joseph H. 1955- Verfasser (DE-588)118906933 aut A friendly introduction to number theory Joseph H. Silverman 4. ed. Boston ; Munich [u.a.] Pearson Education [2014] IX, 409 S. txt rdacontent n rdamedia nc rdacarrier Includes index. Number theory Textbooks 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 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024808353&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 | Silverman, Joseph H. 1955- A friendly introduction to number theory Number theory Textbooks Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4151278-9 |
| title | A friendly introduction to number theory |
| title_auth | A friendly introduction to number theory |
| title_exact_search | A friendly introduction to number theory |
| title_full | A friendly introduction to number theory Joseph H. Silverman |
| title_fullStr | A friendly introduction to number theory Joseph H. Silverman |
| title_full_unstemmed | A friendly introduction to number theory Joseph H. Silverman |
| title_short | A friendly introduction to number theory |
| title_sort | a friendly introduction to number theory |
| topic | Number theory Textbooks Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Number theory Textbooks Zahlentheorie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024808353&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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