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LEADER 02868cam 2200445Ii 4500

001 ocn884538976;

003 OCoLC;

005 20150428113459.0;

008 140724t20142014sz b 001 0 eng d;

020 a| 3319100939;

020 a| 9783319100937;

035 a| (Sirsi) 40024552942;

035 a| 40024552942;

035 a| (OCoLC)884538976;

050 4 a| QA161.E95b| B558 2014;

082 04 a| 512.9222| 23;

100 1 a| Bilu, Yuri F.,e| author.=| ^A1258839;

245 10 a| Problem of Catalan /c| Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte.;

264 1 a| Cham ;a| New York :b| Springer,c| [2014];

300 a| xiv, 245 pages ;c| 25 cm;

336 a| textb| txt2| rdacontent;

337 a| unmediatedb| n2| rdamedia;

338 a| volumeb| nc2| rdacarrier;

504 a| Includes bibliographical references and index.;

505 0 a| 1. An historical account -- 2. Even exponents -- 3. Cassels' relations -- 4. Cyclotomic fields -- 5. Dirichlet L-series and class number formulas -- 6. Higher divisibility theorems -- 7. Gauss sums and Stickelberger's theorem -- 8. Mihăilescu's ideal -- 9. The real part of Mihăilescu's ideal -- 10. Cyclotomic units -- 11. Selmer group and proof of Catalan's conjecture -- 12. The theorem of Thaine -- 13. 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 3 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.;

600 10 a| Mihăilescu, Preda,e| author.=| ^A792661;

600 10 a| Catalan, Eugène Charles,d| 1814-1894.=| ^A916921;

650 0 a| Consecutive powers (Algebra)=| ^A346485;

650 0 a| Problem solving.=| ^A2850;

650 0 a| Number theory.=| ^A22877;

700 1 a| Bugeaud, Yann,d| 1971-e| author.=| ^A589078;

700 1 a| Mignotte, Maurice,e| author.=| ^A256439;

949 i| 30372016578350o| jjlm;

960 o| 1s| 109.00t| Joyner48u| JAPPz| USD;

596 a| 1;

998 a| 3749427;

999 a| QA161 .E95 B558 2014w| LCc| 1i| 30372016578350d| 9/24/2015e| 6/23/2015l| JGESm| JOYNERr| Ys| Yt| JGESBKu| 4/10/2015x| BOOKz| JSTACKSo| .STAFF. jjlm;

Problem of Catalan / Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte.

Author/creator	Bilu, Yuri F. author.
Other author	Bugeaud, Yann, 1971- author.
Other author	Mignotte, Maurice, author.
Format	Book
Publication	Cham ; New York : Springer, [2014]
Copyright Date	©2014
Description	xiv, 245 pages ; 25 cm
Subjects	Mihăilescu, Preda, author. Catalan, Eugène Charles, 1814-1894. Consecutive powers (Algebra) Problem solving. Number theory.

Contents	1. An historical account -- 2. Even exponents -- 3. Cassels' relations -- 4. Cyclotomic fields -- 5. Dirichlet L-series and class number formulas -- 6. Higher divisibility theorems -- 7. Gauss sums and Stickelberger's theorem -- 8. Mihăilescu's ideal -- 9. The real part of Mihăilescu's ideal -- 10. Cyclotomic units -- 11. Selmer group and proof of Catalan's conjecture -- 12. The theorem of Thaine -- 13. 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.
Summary	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.
Bibliography note	Includes bibliographical references and index.
ISBN	3319100939
ISBN	9783319100937

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Problem of Catalan / Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte.

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