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Weak Pseudoprimality Associated with the Generalized Lucas Sequences

In: Approximation and Computation in Science and Engineering

Author

Listed:
  • Dorin Andrica

    (Babeş-Bolyai University)

  • Ovidiu Bagdasar

    (University of Derby)

  • Michael Th. Rassias

    (University of Zurich)

Abstract

Pseudoprimes are composite integers which share properties of the prime numbers, and they have applications in many areas, as, for example, in public-key cryptography. Numerous types of pseudoprimes are known to exist, many of them defined by linear recurrent sequences. In this material, we present some novel classes of pseudoprimes related to the generalized Lucas sequences. First, we present some arithmetic properties of the generalized Lucas and Pell–Lucas sequences and review some classical pseudoprimality notions defined for Fibonacci, Lucas, Pell, and Pell–Lucas sequences and their generalizations. Then we define new notions of pseudoprimality which do not involve the use of the Jacobi symbol and include many classical pseudoprimes. For these, we present associated integer sequences recently added to the Online Encyclopedia of Integer Sequences, identify some key properties, and propose a few conjectures.

Suggested Citation

  • Dorin Andrica & Ovidiu Bagdasar & Michael Th. Rassias, 2022. "Weak Pseudoprimality Associated with the Generalized Lucas Sequences," Springer Optimization and Its Applications, in: Nicholas J. Daras & Themistocles M. Rassias (ed.), Approximation and Computation in Science and Engineering, pages 53-75, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-84122-5_4
    DOI: 10.1007/978-3-030-84122-5_4
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