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[null,"1.","Record Nr.",null,"UNINA9910299981103321"]
[null,null,"Autore",null,"Bilu Yuri F"]
[null,null,"Titolo",null,"The Problem of Catalan / / by Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte"]
[null,null,"Pubbl/distr/stampa",null,"Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014"]
[null,null,"ISBN",null,"3-319-10094-7"]
[null,null,"Edizione",null,"[1st ed. 2014.]"]
[null,null,"Descrizione fisica",null,"1 online resource (251 p.)"]
[null,null,"Disciplina",null,"511/.6"]
[{"$nulls":4},"512.72"]
[null,null,"Soggetti",null,"Number theory"]
[{"$nulls":4},"Algebra"]
[{"$nulls":4},"Number Theory"]
[{"$nulls":4},"General Algebraic Systems"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and indexes."]
[null,null,"Nota di contenuto",null,"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."]
[null,null,null,"Sommario/riassunto","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."]