Baker’s Method and Tijdeman’s Argument

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 13 in The Problem of Catalan, 2014, pp 159-233 from Springer

Abstract: Abstract This chapter is somewhat isolated and can be read (almost) independently of the others. We discuss in it the application of Baker’s method to Diophantine equations of Catalan type. We give a brief introduction to this method, show how it applies to classical Diophantine equations, and reproduce the beautiful argument of Tijdeman, who proved that Catalan’s equation has only finitely many solutions. Moreover, the solutions are bounded by an absolute effective constant (that is, a constant that can, in principle, be explicitly determined), which reduces the problem to a finite computation. Before the work of Mihăilescu this was the top achievement on Catalan’s problem.We also consider the more general equation of Pillai and show that it has finitely many solutions when one of the four variables is fixed.

Keywords: Tijdeman; Classical Diophantine Equations; Beautiful Argument; Superelliptic Equation; Finitely-generated Group (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_13

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DOI: 10.1007/978-3-319-10094-4_13

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