The Problem of Catalan

Bilu, Yuri F.; Bugeaud, Yann; Mignotte, Maurice

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.

Details

Published by: Springer

Publication Date: 2014-10-27

Format: Hardcover

ISBN-13: 9783319100937

DOI: 10.1007/978-3-319-10094-4

Dimensions: 235cm x155cm

Pages: 245