The Problem of Catalan

• Κύριοι συγγραφείς: Bilu, Yuri F. (Συγγραφέας), Bugeaud, Yann (Συγγραφέας), Mignotte, Maurice (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Θέματα: Mathematics.; Algebra.; Number theory.; Number Theory.; General Algebraic Systems.

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 (almo...

Πίνακας περιεχομένων:

• 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.