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The Problem of Catalan
In 1842 the Belgian mathematician Eugène Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers. 160 years after, the question was answered affirmatively by the Swiss mathematician of Romanian origin Preda Mihăilescu. In this book we give a complete and (al...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Springer,
2014.
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| Edición: | 1st ed. 2014. |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-3-319-10094-4 | ||
| 003 | DE-He213 | ||
| 005 | 20220115010432.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 141009s2014 sz | s |||| 0|eng d | ||
| 020 | |a 9783319100944 |9 978-3-319-10094-4 | ||
| 024 | 7 | |a 10.1007/978-3-319-10094-4 |2 doi | |
| 050 | 4 | |a QA241-247.5 | |
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| 072 | 7 | |a MAT022000 |2 bisacsh | |
| 072 | 7 | |a PBH |2 thema | |
| 082 | 0 | 4 | |a 512.7 |2 23 |
| 100 | 1 | |a Bilu, Yuri F. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 4 | |a The Problem of Catalan |h [electronic resource] / |c by Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte. |
| 250 | |a 1st ed. 2014. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2014. | |
| 300 | |a XIV, 245 p. 3 illus. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 505 | 0 | |a An Historical Account -- Even Exponents -- Cassels' Relations -- Cyclotomic Fields -- Dirichlet L-Series and Class Number Formulas -- Higher Divisibility Theorems -- Gauss Sums and Stickelberger's Theorem -- Mihăilescu's Ideal -- The Real Part of Mihăilescu's Ideal -- Cyclotomic units -- Selmer Group and Proof of Catalan's Conjecture -- The Theorem of Thaine -- Baker's Method and Tijdeman's Argument -- Appendix A: Number Fields -- Appendix B: Heights -- Appendix C: Commutative Rings, Modules, Semi-Simplicity -- Appendix D: Group Rings and Characters -- Appendix E: Reduction and Torsion of Finite G-Modules -- Appendix F: Radical Extensions. | |
| 520 | |a In 1842 the Belgian mathematician Eugène Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers. 160 years after, the question was answered affirmatively by the Swiss mathematician of Romanian origin Preda Mihăilescu. In this book we give a complete and (almost) self-contained exposition of Mihăilescu's work, which must be understandable by a curious university student, not necessarily specializing in Number Theory. We assume very modest background: a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory. | ||
| 650 | 0 | |a Number theory. | |
| 650 | 0 | |a Universal algebra. | |
| 650 | 0 | |a Algebra. | |
| 650 | 1 | 4 | |a Number Theory. |
| 650 | 2 | 4 | |a General Algebraic Systems. |
| 650 | 2 | 4 | |a Algebra. |
| 700 | 1 | |a Bugeaud, Yann. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Mignotte, Maurice. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783319100951 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319100937 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319362557 |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-319-10094-4 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||