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UNE CONJECTURE DE LEBESGUE

Published online by Cambridge University Press:  29 March 2004

EMMANUEL HALBERSTADT  and
ALAIN KRAUS
EMMANUEL HALBERSTADT
Affiliation:
Institut de Mathématiques, UMR 7586 du CNRS, Équipe de Théorie des Nombres, Université de Paris VI, 175 Rue du Chevaleret, Paris 75013, Francehalberst@math.jussieu.fr
ALAIN KRAUS
Affiliation:
Institut de Mathématiques, UMR 7586 du CNRS, Équipe de Théorie des Nombres, Université de Paris VI, 175 Rue du Chevaleret, Paris 75013, Francekraus@math.jussieu.fr
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Abstract

Let $A > 0$ be an integer. The equation $x^5 - y^5 = Az^5$ was first studied by Dirichlet and Lebesgue. Lebesgue conjectured in 1843 that if $A$ has no prime divisors of the form $10k+1$, the equation has no solutions except the visible ones. Partial results were obtained by Lebesgue and by Terjanian in 1987. The purpose of the paper is to prove Lebesgue's conjecture. The main tool used is the method known as the elliptic Chabauty method.

Keywords

11G11D41
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 2 , April 2004 , pp. 291 - 302
Copyright
The London Mathematical Society 2004

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