On Some New Arithmetic Properties of the Generalized Lucas Sequences


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

Mathematics Subject Classification

  • 11A51
  • 11B39
  • 11B50