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Article Dans Une Revue Communications in Mathematics Année : 2020

Solutions of the Diophantine Equation 7X2 + Y 7 = Z2 from Recurrence Sequences

Hayder R. Hashim
  • Fonction : Auteur correspondant

Résumé

Consider the system x 2 − ay 2 = b, P (x, y) = z 2, where P is a given integer polynomial. Historically, the integer solutions of such systems have been investigated by many authors using the congruence arguments and the quadratic reciprocity. In this paper, we use Kedlaya’s procedure and the techniques of using congruence arguments with the quadratic reciprocity to investigate the solutions of the Diophantine equation 7X 2 + Y 7 = Z 2 if (X, Y) = (L n , F n ) (or (X, Y) = (F n , L n )) where {F n } and {L n } represent the sequences of Fibonacci numbers and Lucas numbers respectively.
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hal-03664981 , version 1 (11-05-2022)

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Paternité - Pas d'utilisation commerciale - Pas de modification

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Hayder R. Hashim. Solutions of the Diophantine Equation 7X2 + Y 7 = Z2 from Recurrence Sequences. Communications in Mathematics, 2020, Volume 28 (2020), Issue 1 (1), pp.55 - 66. ⟨10.2478/cm-2020-0005⟩. ⟨hal-03664981⟩
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