π The Problem of Catalan
Tuesday, November 27, 2018 by dev
The Problem of Catalan
By:Yuri Bilu,Yann Bugeaud,Maurice Mignotte
Published on 2014-10-09 by Springer
In 1842 the Belgian mathematician EugΓ¨ne 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 MihΔilescu. 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 MihΔilescu’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.
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Book which was published by Springer since 2014-10-09 have ISBNs, ISBN 13 Code is 9783319100944 and ISBN 10 Code is 3319100947
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