The Problem of Catalan - Couverture souple

Bilu, Yuri F.

Couverture souple

ISBN 10 : 3319362550 ISBN 13 : 9783319362557

Editeur : Springer, 2016

Synopsis

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 other words, 3² - 2³ = 1 is the only solution of the equation x^p - y^q = 1 in integers x, y, p, q with xy 0 and p, q >= 2.

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 a very modest background: a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2016
• Langue: anglais
• ISBN 10: 3319362550
• ISBN 13: 9783319362557
• Reliure: Broché
• Nombre de pages: 260
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Tiergartenstr. 17; Heidelberg; 69121; Allemagne