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Un nouveau critère pour l'équation de Catalan

Part of: Diophantine equations

Published online by Cambridge University Press:  26 February 2010

Yann Bugeaud  and
Guillaume Hanrot
Yann Bugeaud
Affiliation:
Université Louis Pasteur, U. F. R. de mathématiques, 7, rue René Descartes, F-67084 Strasbourg, France. E-mail: bugeaud@math.u-strasbg.fr
Guillaume Hanrot
Affiliation:
Projet POLKA, INRIA Lorraine, 615, rue du Jardin Botanique, B.P. 101, F-54602 Villers-lès-Nancy Cedex, France. E-mail: guillaume.hanrot@loria.fr
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Abstract

A new criterion on Catalan's equation is proved by elementary means

This shows, without appealing either to the theory of linear forms in logarithms, or to any computation, that (C) has no solution (x, y, p, q) with min {p, q}≤41, except (3,2, 2, 3).

Résumé

On démontre de manière élémentaire un nouveau critère pour l'équation de Catalan

II permet de prouver, sans faire appel à la théorie des formes linéaires de logarithmes ni au moindre calcul, qu'outre (3, 2, 2, 3), toute éventuelle solution (x, y, p, q) de (C) vérifie min {p, q}≥43.

MSC classification

Secondary: 11D61: Exponential equations

Information

Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000 , pp. 63 - 73
Copyright
Copyright © University College London 2000

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