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hal-00129723, version 1

On the number of solutions of simultaneous Pell equations

Mihai Cipu 1, Maurice Mignotte 1

(2006-02-10)

Abstract: It is proved that two Pell equations have at most two solutions in positive integers. This is the best possible result, since there are examples of pairs of Pell equations having two positive solutions.

  • 1:  Institut de Recherche Mathématique Avancée (IRMA)
  • CNRS : UMR7501 – Université Louis Pasteur - Strasbourg I
  • Domain : Mathematics/Number Theory
  • Keywords : "Pell equation – linear form in logarithms – simultaneous Diophantine equations"
 
  • hal-00129723, version 1
  • http://hal.archives-ouvertes.fr/hal-00129723
  • oai:hal.archives-ouvertes.fr:hal-00129723
  • From: Véronique Bertrand <>
  • Submitted on: Thursday, 8 February 2007 15:09:01
  • Updated on: Thursday, 8 February 2007 17:07:28