The higher arithmetic: an introduction to the theory of numbers
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Ausgabe: | 8. ed |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 239 S. |
| ISBN: | 9780521722360 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV035175792 | ||
| 003 | DE-604 | ||
| 005 | 20090122 | ||
| 007 | t | ||
| 008 | 081124s2008 |||| 00||| eng d | ||
| 020 | |a 9780521722360 |9 978-0-521-72236-0 | ||
| 035 | |a (OCoLC)213400639 | ||
| 035 | |a (DE-599)BVBBV035175792 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-11 |a DE-83 |a DE-19 | ||
| 050 | 0 | |a QA241 | |
| 082 | 0 | |a 512.7 |2 22 | |
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 084 | |a 11-01 |2 msc | ||
| 100 | 1 | |a Davenport, Harold |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The higher arithmetic |b an introduction to the theory of numbers |c H. Davenport |
| 250 | |a 8. ed | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a IX, 239 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Number theory | |
| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Arithmetik |0 (DE-588)4002919-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Zahlentheorie |0 (DE-588)4067277-3 |D s |
| 689 | 0 | 1 | |a Arithmetik |0 (DE-588)4002919-0 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016982643&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016982643 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804138346221404160 |
|---|---|
| adam_text | CONTENTS
Introduction page
viii
I Factorization and the Primes
1
1.
The laws of arithmetic
1
2.
Proof by induction
6
3.
Prime numbers
8
4.
The fundamental theorem of arithmetic
9
5.
Consequences of the fundamental theorem
12
6.
Euclid s algorithm
16
7.
Another proof of the fundamental theorem
18
8.
A property of the H.C.F
19
9.
Factorizing a number
22
10. Theseries
of primes
25
II Congruences
31
1.
The congruence notation
31
2.
Linear congruences
33
3.
Fermat s theorem
35
4.
Euler s function
ф(т)
37
5.
Wilson s theorem
40
6.
Algebraic congruences
41
7.
Congruences to a prime modulus
42
8.
Congruences in several unknowns
45
9.
Congruences covering all numbers
46
Contents
[II
Quadratic Residues
49
1.
Primitive roots
49
2.
Indices
53
3.
Quadratic residues
55
4.
Gauss s lemma
58
5.
The law of reciprocity
59
6.
The distribution of the quadratic residues
63
IV Continued Fractions
68
1.
Introduction
68
2.
The general continued fraction
70
3.
Euler s rale
72
4.
The
convergents
to a continued fraction
74
5.
The equation ax
—
by
= 1
77
6.
Infinite continued fractions
78
7.
Diophantine approximation
82
8.
Quadratic irrationals
83
9.
Purely periodic continued fractions
86
10.
Lagrange s theorem
92
11.
Pell s equation
94
12.
A geometrical interpretation of continued
fractions
99
V Sums of Squares
103
1.
Numbers representable by two squares
103
2.
Primes of the form 4k
+ 1
104
3.
Constructions for
χ
and
y
108
4.
Representation by four squares
111
5.
Representation by three squares
114
VI Quadratic Forms
116
I. Introduction
116
2.
Equivalent forms
117
3.
The discriminant
120
4.
The representation of a number by a form
122
5.
Three examples
124
6.
The reduction of positive definite forms
126
7.
The reduced forms
128
8.
The number of representations
131
9.
The class-number
133
Contents
vii
VII Some Diophantine
Equations
137
1.
Introduction
137
2.
The equation
χ2
+
y2
—
ζ2
138
3.
The equation ax2
+
by2
=
z2
140
4.
Elliptic equations and curves
145
5.
Elliptic equations modulo primes
151
6.
Fermaťs
Last Theorem
154
7.
The equation x3
+
y3
=
z3
+
u/3 1
57
8.
Further developments
159
VIII
Computers and Number Theory
165
1.
Introduction
165
2.
Testing for primality
168
3.
Random number generators
173
4.
Pollard s factoring methods
179
5.
Factoring and primality via elliptic curves
185
6.
Factoring large numbers
188
7.
The Diffie-Hellman cryptographic method
194
8.
The RSA cryptographic method
199
9.
Primality testing revisited
200
Exercises
209
Hints
222
Answers
225
Bibliography
235
index
237
|
| adam_txt |
CONTENTS
Introduction page
viii
I Factorization and the Primes
1
1.
The laws of arithmetic
1
2.
Proof by induction
6
3.
Prime numbers
8
4.
The fundamental theorem of arithmetic
9
5.
Consequences of the fundamental theorem
12
6.
Euclid's algorithm
16
7.
Another proof of the fundamental theorem
18
8.
A property of the H.C.F
19
9.
Factorizing a number
22
10. Theseries
of primes
25
II Congruences
31
1.
The congruence notation
31
2.
Linear congruences
33
3.
Fermat's theorem
35
4.
Euler's function
ф(т)
37
5.
Wilson's theorem
40
6.
Algebraic congruences
41
7.
Congruences to a prime modulus
42
8.
Congruences in several unknowns
45
9.
Congruences covering all numbers
46
Contents
[II
Quadratic Residues
49
1.
Primitive roots
49
2.
Indices
53
3.
Quadratic residues
55
4.
Gauss's lemma
58
5.
The law of reciprocity
59
6.
The distribution of the quadratic residues
63
IV Continued Fractions
68
1.
Introduction
68
2.
The general continued fraction
70
3.
Euler's rale
72
4.
The
convergents
to a continued fraction
74
5.
The equation ax
—
by
= 1
77
6.
Infinite continued fractions
78
7.
Diophantine approximation
82
8.
Quadratic irrationals
83
9.
Purely periodic continued fractions
86
10.
Lagrange's theorem
92
11.
Pell's equation
94
12.
A geometrical interpretation of continued
fractions
99
V Sums of Squares
103
1.
Numbers representable by two squares
103
2.
Primes of the form 4k
+ 1
104
3.
Constructions for
χ
and
y
108
4.
Representation by four squares
111
5.
Representation by three squares
114
VI Quadratic Forms
116
I. Introduction
116
2.
Equivalent forms
117
3.
The discriminant
120
4.
The representation of a number by a form
122
5.
Three examples
124
6.
The reduction of positive definite forms
126
7.
The reduced forms
128
8.
The number of representations
131
9.
The class-number
133
Contents
vii
VII Some Diophantine
Equations
137
1.
Introduction
137
2.
The equation
χ2
+
y2
—
ζ2
138
3.
The equation ax2
+
by2
=
z2
140
4.
Elliptic equations and curves
145
5.
Elliptic equations modulo primes
151
6.
Fermaťs
Last Theorem
154
7.
The equation x3
+
y3
=
z3
+
u/3 1
57
8.
Further developments
159
VIII
Computers and Number Theory
165
1.
Introduction
165
2.
Testing for primality
168
3.
'Random'number generators
173
4.
Pollard's factoring methods
179
5.
Factoring and primality via elliptic curves
185
6.
Factoring large numbers
188
7.
The Diffie-Hellman cryptographic method
194
8.
The RSA cryptographic method
199
9.
Primality testing revisited
200
Exercises
209
Hints
222
Answers
225
Bibliography
235
index
237 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Davenport, Harold |
| author_facet | Davenport, Harold |
| author_role | aut |
| author_sort | Davenport, Harold |
| author_variant | h d hd |
| building | Verbundindex |
| bvnumber | BV035175792 |
| callnumber-first | Q - Science |
| callnumber-label | QA241 |
| callnumber-raw | QA241 |
| callnumber-search | QA241 |
| callnumber-sort | QA 3241 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)213400639 (DE-599)BVBBV035175792 |
| 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 | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 8. ed |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01534nam a2200409 c 4500</leader><controlfield tag="001">BV035175792</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20090122 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">081124s2008 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780521722360</subfield><subfield code="9">978-0-521-72236-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)213400639</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV035175792</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-19</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA241</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.7</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="0">(DE-625)143222:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">11-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Davenport, Harold</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The higher arithmetic</subfield><subfield code="b">an introduction to the theory of numbers</subfield><subfield code="c">H. Davenport</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">8. ed</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge [u.a.]</subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">2008</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">IX, 239 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Arithmetik</subfield><subfield code="0">(DE-588)4002919-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Arithmetik</subfield><subfield code="0">(DE-588)4002919-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016982643&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016982643</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV035175792 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:56:03Z |
| indexdate | 2024-07-09T21:26:43Z |
| institution | BVB |
| isbn | 9780521722360 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016982643 |
| oclc_num | 213400639 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 DE-83 DE-19 DE-BY-UBM |
| owner_facet | DE-355 DE-BY-UBR DE-11 DE-83 DE-19 DE-BY-UBM |
| physical | IX, 239 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Davenport, Harold Verfasser aut The higher arithmetic an introduction to the theory of numbers H. Davenport 8. ed Cambridge [u.a.] Cambridge Univ. Press 2008 IX, 239 S. txt rdacontent n rdamedia nc rdacarrier Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Arithmetik (DE-588)4002919-0 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s Arithmetik (DE-588)4002919-0 s 1\p DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016982643&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 | Davenport, Harold The higher arithmetic an introduction to the theory of numbers Number theory Zahlentheorie (DE-588)4067277-3 gnd Arithmetik (DE-588)4002919-0 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4002919-0 |
| title | The higher arithmetic an introduction to the theory of numbers |
| title_auth | The higher arithmetic an introduction to the theory of numbers |
| title_exact_search | The higher arithmetic an introduction to the theory of numbers |
| title_exact_search_txtP | The higher arithmetic an introduction to the theory of numbers |
| title_full | The higher arithmetic an introduction to the theory of numbers H. Davenport |
| title_fullStr | The higher arithmetic an introduction to the theory of numbers H. Davenport |
| title_full_unstemmed | The higher arithmetic an introduction to the theory of numbers H. Davenport |
| title_short | The higher arithmetic |
| title_sort | the higher arithmetic an introduction to the theory of numbers |
| title_sub | an introduction to the theory of numbers |
| topic | Number theory Zahlentheorie (DE-588)4067277-3 gnd Arithmetik (DE-588)4002919-0 gnd |
| topic_facet | Number theory Zahlentheorie Arithmetik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016982643&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT davenportharold thehigherarithmeticanintroductiontothetheoryofnumbers |