The Problem of Catalan By: Yuri F. Bilu; Yann Bugeaud; Maurice Mignotte Publisher: Springer Print ISBN: 9783319100937, 3319100939 eText ISBN: 9783319100944, 3319100947 Copyright year: 2014 Format: EPUB Available from $ 99.00 USD SKU 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 other words, 32 – 23 = 1 is the only solution of the equation xp – yq = 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. Download eBook Free: https://ouo.io/OzMssl
