The Problem of Catalan - E-book

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The Problem Of Catalan - ENG

Yuri F. Bilu; Yann Bugeaud; Maurice Mignotte

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Sinopsis

ISBN:	9783319100944
Formato:	ePub
Idioma:	Inglés
Editorial:	Springer Nature
Tema:	Matemáticas
Subtema:	Teoría dos Números
Año de publicación:	2014-10-09

In 1842 the Belgian mathematician EugÃ¨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 MihÄƒilescu. In other words, 32 â€“ 23 = 1 is the only solution of the equation xp â€“ yq = 1 in integers x, y, p, q with xy â‰ 0 and p, q â‰¥ 2. In this book we give a complete and (almost) self-contained exposition of MihÄƒilescu 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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