On Some New Arithmetic Properties of the Generalized Lucas Sequences

Mediterranean Journal of Mathematics volume 18, Article number: 47 (2021) Cite this article

Abstract

Some arithmetic properties of the generalized Lucas sequences are studied, extending a number of recent results obtained for Fibonacci, Lucas, Pell, and Pell–Lucas sequences. These properties are then applied to investigate certain notions of Fibonacci, Lucas, Pell, and Pell–Lucas pseudoprimality, for which we formulate some conjectures.

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Author information

Affiliations

  1. Faculty of Mathematics and Computer Science, Babeş-Bolyai University of Cluj-Napoca, Kogălniceanu Street, Nr. 1, 400084, Cluj-Napoca, Romania

    Dorin Andrica

  2. School of Computing and Engineering, University of Derby, Markeaton Street, Derby, DE22 3BD, UK

    Ovidiu Bagdasar

Authors
  1. Dorin Andrica
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  2. Ovidiu Bagdasar
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Correspondence to Ovidiu Bagdasar.

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Andrica, D., Bagdasar, O. On Some New Arithmetic Properties of the Generalized Lucas Sequences. Mediterr. J. Math. 18, 47 (2021). https://doi.org/10.1007/s00009-020-01653-w

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Keywords

  • Generalized Lucas sequences
  • Pell sequence
  • Pell–Lucas sequence
  • Legendre symbol
  • Pseudoprimality

Mathematics Subject Classification

  • 11A51
  • 11B39
  • 11B50