13 lectures on Fermat's last theorem:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
[1996]
|
| Edition: | [3. Dr.] |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XVI, 308 S. Ill. |
| ISBN: | 0387904328 3540904328 |
Staff View
MARC
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| 245 | 1 | 0 | |a 13 lectures on Fermat's last theorem |c Paulo Ribenboim |
| 250 | |a [3. Dr.] | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c [1996] | |
| 300 | |a XVI, 308 S. |b Ill. | ||
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| 337 | |b n |2 rdamedia | ||
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| 700 | 1 | 2 | |a Ribenboim, Paulo |d 1928- |0 (DE-588)117719404 |4 aut |t Thirteen lectures on Fermat's last theorem |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007130666&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Record in the Search Index
| _version_ | 1807502127592898560 |
|---|---|
| adam_text |
CONTENTS
LECTURE
I
THE
EARLY
HISTORY
OF
FERMAT
'
S
LAST
THEOREM
1
1
THE
PROBLEM
1
2
EARLY
ATTEMPTS
4
3
KUMMER
'
S
MONUMENTAL
THEOREM
6
4
REGULAR
PRIMES
9
5
KUMMER
'
S
WORK
ON
IRREGULAR
PRIME
EXPONENTS
10
6
OTHER
RELEVANT
RESULTS
12
7
THE
GOLDEN
MEDAL
AND
THE
WOLFSKEHL
PRIZE
13
BIBLIOGRAPHY
16
LECTURE
II
RECENT
RESULTS
19
1
STATING
THE
RESULTS
19
2
EXPLANATIONS
21
BIBLIOGRAPHY
29
LECTURE
III
B.K.
=
BEFORE
KUMMER
35
1
THE
PYTHAGOREAN
EQUATION
36
2
THE
BIQUADRATIC
EQUATION
37
3
THE
CUBIC
EQUATION
39
4
THE
QUINTIC
EQUATION
45
5
FERMAT
'
S
EQUATION
OF
DEGREE
SEVEN
46
BIBLIOGRAPHY
47
XIV
CONTENTS
LECTURE
IV
THE
NAIVE
APPROACH
51
1
THE
RELATIONS
OF
BARLOW
AND
ABEL
51
2
SOPHIE
GERMAIN
54
3
CONGRUENCES
57
4
WENDT
'
S
THEOREM
61
5
ABEL
'
S
CONJECTURE
63
6
FERMAT
'
S
EQUATION
WITH
EVEN
EXPONENT
65
7
ODDS
AND
ENDS
69
BIBLIOGRAPHY
70
LECTURE
V
KUMMER
'
S
MONUMENT
75
1
A
JUSTIFICATION
OF
KUMMER
'
S
METHOD
75
2
BASIC
FACTS
ABOUT
THE
ARITHMETIC
OF
CYCLOTOMIC
FIELDS
77
3
KUMMER
'
S
MAIN
THEOREM
82
BIBLIOGRAPHY
90
LECTURE
VI
REGULAR
PRIMES
93
1
THE
CLASS
NUMBER
OF
CYCLOTOMIC
FIELDS
93
2
BERNOULLI
NUMBERS
AND
KUMMER
'
S
REGULARITY
CRITERION
99
3
VARIOUS
ARITHMETIC
PROPERTIES
OF
BERNOULLI
NUMBERS
103
4
THE
ABUNDANCE
OF
IRREGULAR
PRIMES
106
5
COMPUTATION
OF
IRREGULAR
PRIMES
107
BIBLIOGRAPHY
111
LECTURE
VII
KUMMER
EXITS
115
1
THE
PERIODS
OF
THE
CYCLOTOMIC
EQUATION
115
2
THE
JACOBI
CYCLOTOMIC
FUNCTION
117
3
ON
THE
GENERATION
OF
THE
CLASS
GROUP
OF
THE
CYCLOTOMIC
FIELD
119
4
KUMMER
'
S
CONGRUENCES
120
5
KUMMER
'
S
THEOREM
FOR
A
CLASS
OF
IRREGULAR
PRIMES
126
6
COMPUTATIONS
OF
THE
CLASS
NUMBER
130
BIBLIOGRAPHY
134
LECTURE
VIII
AFTER
KUMMER,
A
NEW
LIGHT
139
1
THE
CONGRUENCES
OF
MIRIMANOFF
139
2
THE
THEOREM
OF
KRASNER
148
3
THE
THEOREMS
OF
WIEFERICH
AND
MIRIMANOFF
151
4
FERMAT
'
S
THEOREM
AND
THE
MERSENNE
PRIMES
154
5
SUMMATION
CRITERIA
155
6
FERMAT
QUOTIENT
CRITERIA
159
BIBLIOGRAPHY
161
CONTENTS
XV
LECTURE
IX
THE
POWER
OF
CLASS
FIELD
THEORY
165
1
THE
POWER
RESIDUE
SYMBOL
165
2
KUMMER
EXTENSIONS
167
3
THE
MAIN
THEOREMS
OF
FURTWANGLER
168
4
THE
METHOD
OF
SINGULAR
INTEGERS
170
5
HASSE
172
6
THE
P-RANK
OF
THE
CLASS
GROUP
OF
THE
CYCLOTOMIC
FIELD
178
7
CRITERIA
OF
^-DIVISIBILITY
OF
THE
CLASS
NUMBER
184
8
PROPERLY
AND
IMPROPERLY
IRREGULAR
CYCLOTOMIC
FIELDS
188
BIBLIOGRAPHY
193
LECTURE
X
FRESH
EFFORTS
199
1
FERMAT
'
S
LAST
THEOREM
IS
TRUE
FOR
EVERY
PRIME
EXPONENT
LESS
THAN
125000
199
2
EULER
NUMBERS
AND
FERMAT
'
S
THEOREM
202
3
THE
FIRST
CASE
IS
TRUE
FOR
INFINITELY
MANY
PAIRWISE
RELATIVELY
PRIME
EXPONENTS
205
4
CONNECTIONS
BETWEEN
ELLIPTIC
CURVES
AND
FERMAT
'
S
THEOREM
207
5
IWASAWA
'
S
THEORY
209
6
THE
FERMAT
FUNCTION
FIELD
211
7
MORDELL
'
S
CONJECTURE
214
8
THE
LOGICIANS
216
BIBLIOGRAPHY
218
LECTURE
XI
ESTIMATES
225
1
ELEMENTARY
(AND
NOT
SO
ELEMENTARY)
ESTIMATES
225
2
ESTIMATES
BASED
ON
THE
CRITERIA
INVOLVING
FERMAT
QUOTIENTS
229
3
THUE,
ROTH,
SIEGEL
AND
BAKER
232
4
APPLICATIONS
OF
THE
NEW
METHODS
237
BIBLIOGRAPHY
241
LECTURE
XII
FERMAT
'
S
CONGRUENCE
245
1
FERMAT
'
S
THEOREM
OVER
PRIME
FIELDS
245
2
THE
LOCAL
FERMAT
'
S
THEOREM
251
3
THE
PROBLEM
MODULO
A
PRIME-POWER
253
BIBLIOGRAPHY
260
LECTURE
XIII
VARIATIONS
AND
FUGUE
ON
A
THEME
263
1
VARIATION
I
(IN
THE
TONE
OF
POLYNOMIAL
FUNCTIONS)
263
2
VARIATION
II
(IN
THE
TONE
OF
ENTIRE
FUNCTIONS)
265
XVI
CONTENTS
3
VARIATION
III
(IN
THE
THETA
TONE)
266
4
VARIATION
IV
(IN
THE
TONE
OF
DIFFERENTIAL
EQUATIONS)
270
5
VARIATION
V
(GIOCOSO)
271
6
VARIATION
VI
(IN
THE
NEGATIVE
TONE)
272
7
VARIATION
VII
(IN
THE
ORDINAL
TONE)
273
8
VARIATION
VIII
(IN
A
NONASSOCIATIVE
TONE)
273
9
VARIATION
IX
(IN
THE
MATRIX
TONE)
275
10
FUGUE
(IN
THE
QUADRATIC
TONE)
277
BIBLIOGRAPHY
286
EPILOGUE
291
INDEX
OF
NAMES
299
SUBJECT
INDEX
305 |
| any_adam_object | 1 |
| author | Ribenboim, Paulo 1928- Ribenboim, Paulo 1928- |
| author_GND | (DE-588)117719404 |
| author_facet | Ribenboim, Paulo 1928- Ribenboim, Paulo 1928- |
| author_role | aut aut |
| author_sort | Ribenboim, Paulo 1928- |
| author_variant | p r pr p r pr |
| building | Verbundindex |
| bvnumber | BV010683337 |
| classification_rvk | SK 180 |
| classification_tum | MAT 102f |
| ctrlnum | (OCoLC)440775237 (DE-599)BVBBV010683337 |
| discipline | Mathematik |
| edition | [3. Dr.] |
| format | Book |
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| id | DE-604.BV010683337 |
| illustrated | Illustrated |
| indexdate | 2024-08-16T00:32:35Z |
| institution | BVB |
| isbn | 0387904328 3540904328 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007130666 |
| oclc_num | 440775237 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-1046 |
| owner_facet | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-1046 |
| physical | XVI, 308 S. Ill. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| spelling | Ribenboim, Paulo 1928- Verfasser (DE-588)117719404 aut Sammlung 13 lectures on Fermat's last theorem Paulo Ribenboim [3. Dr.] New York [u.a.] Springer [1996] XVI, 308 S. Ill. txt rdacontent n rdamedia nc rdacarrier Literaturangaben teorija števil - algebraična števila Fermatsche Vermutung (DE-588)4154012-8 gnd rswk-swf Fermatsche Vermutung (DE-588)4154012-8 s DE-604 Ribenboim, Paulo 1928- (DE-588)117719404 aut Thirteen lectures on Fermat's last theorem DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007130666&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ribenboim, Paulo 1928- Ribenboim, Paulo 1928- 13 lectures on Fermat's last theorem teorija števil - algebraična števila Fermatsche Vermutung (DE-588)4154012-8 gnd |
| subject_GND | (DE-588)4154012-8 |
| title | 13 lectures on Fermat's last theorem |
| title_alt | Thirteen lectures on Fermat's last theorem |
| title_auth | 13 lectures on Fermat's last theorem |
| title_exact_search | 13 lectures on Fermat's last theorem |
| title_full | 13 lectures on Fermat's last theorem Paulo Ribenboim |
| title_fullStr | 13 lectures on Fermat's last theorem Paulo Ribenboim |
| title_full_unstemmed | 13 lectures on Fermat's last theorem Paulo Ribenboim |
| title_short | 13 lectures on Fermat's last theorem |
| title_sort | 13 lectures on fermat s last theorem |
| topic | teorija števil - algebraična števila Fermatsche Vermutung (DE-588)4154012-8 gnd |
| topic_facet | teorija števil - algebraična števila Fermatsche Vermutung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007130666&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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