Even Exponents

Yuri F. Bilu, Yann Bugeaud and Maurice Mignotte
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Yuri F. Bilu: University of Bordeaux and CNRS, Institute of Mathematics of Bordeaux
Yann Bugeaud: University of Strasbourg and CNRS, IRMA, Mathematical Institute
Maurice Mignotte: University of Strasbourg and CNRS, IRMA, Mathematical Institute

Chapter Chapter 2 in The Problem of Catalan, 2014, pp 11-25 from Springer

Abstract: Abstract In this chapter we consider Catalan’s equation x p − y q = 1 when one of the exponents p and q is even. This reduces to the case when one of p and q is equal to 2 and the other is an odd prime number. We prove the theorems of Lebesgue, Ko Chao, and Euler, which imply that the only nontrivial solution of the equation x 2 − y q = ±1 is 32 − 23 = 1.

Keywords: Elliptic Curve; Nontrivial Solution; Diophantine Equation; Positive Unit; Cyclotomic Field (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-10094-4_2

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DOI: 10.1007/978-3-319-10094-4_2

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