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.
• Φυσική περιγραφή: XIV, 245 p. 3 illus. online resource.
• ISBN: 9783319100944

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.