Diophantine equations involving the bi-periodic Fibonacci and Lucas sequences

Lyes AIT-AMRANE; Djilali BEHLOUL; Akila DJOUMAKH

doi:10.12697/ACUTM.2022.26.09

Lyes AIT-AMRANE Ecole nationale Supérieure d’Informatique (ESI)
Djilali BEHLOUL University of Science and Technology Houari Boumediene
Akila DJOUMAKH University of Science and Technology Houari Boumediene

DOI: https://doi.org/10.12697/ACUTM.2022.26.09

Keywords: Bi-periodic Fibonacci sequence, bi-periodic Lucas sequence, Diophantine equation, Pell’s equation

Abstract

In this paper, we present new identities involving the biperiodic Fibonacci and Lucas sequences. Then we solve completely some quadratic Diophantine equations involving the bi-periodic Fibonacci and Lucas sequences.

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Author Biographies

Lyes AIT-AMRANE, Ecole nationale Supérieure d’Informatique (ESI)

LATN laboratory, Faculty of Mathematics

Djilali BEHLOUL, University of Science and Technology Houari Boumediene

Faculty of Computer Science

Akila DJOUMAKH, University of Science and Technology Houari Boumediene

Faculty of Mathematics