The Problem of Catalan by Yuri F. Bilu, Hardcover | Indigo Chapters

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 MihÄilescu. In other words, 32- 23= 1 is the only solution of the equationxp-yq= 1 in integersx, y, p, qwithxy' 0 andp, q'¥2.In this book we give a complete and (almost) self-contained exposition of MihÄilescu'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. | The Problem of Catalan by Yuri F. Bilu, Hardcover | Indigo Chapters