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Comptes Rendus Mathématique
Volume 339, n° 5
pages 327-330 (septembre 2004)
Doi : 10.1016/j.crma.2004.06.007
Received : 27 May 2004 ;  accepted : 18 June 2004
Sur les nombres de Fibonacci de la forme  
On Fibonacci numbers of the form  .
 

Yann Bugeaud a , Maurice Mignotte a , Samir Siksek b
a Université Louis Pasteur, U.F.R. de mathématiques, 7, rue René Descartes, 67084 Strasbourg cedex, France 
b Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, PO Box 36, Al-Khod 123, Oman 

Résumé

Nous étudions lʼéquation   où q est un nombre premier et k un entier positif. Nous la résolvons pour tous les   et obtenons des conditions nécessaires lorsque  . En particulier, nous répondons à une question de Ribenboim concernant lʼéquation  . Pour citer cet article : Y. Bugeaud et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).

The full text of this article is available in PDF format.
Abstract

We study the equation   where q is a prime number and k is a positive integer. We solve it for all   and get partial results when  . In particular, we answer Ribenboimʼs question about  . To cite this article: Y. Bugeaud et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).

The full text of this article is available in PDF format.


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