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On Generalized Lucas Pseudoprimality of Level k

Author

Listed:
  • Dorin Andrica

    (Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania)

  • Ovidiu Bagdasar

    (School of Computing and Engineering, University of Derby, Derby DE22 1GB, UK)

Abstract

We investigate the Fibonacci pseudoprimes of level k , and we disprove a statement concerning the relationship between the sets of different levels, and also discuss a counterpart of this result for the Lucas pseudoprimes of level k . We then use some recent arithmetic properties of the generalized Lucas, and generalized Pell–Lucas sequences, to define some new types of pseudoprimes of levels k + and k − and parameter a . For these novel pseudoprime sequences we investigate some basic properties and calculate numerous associated integer sequences which we have added to the Online Encyclopedia of Integer Sequences.

Suggested Citation

  • Dorin Andrica & Ovidiu Bagdasar, 2021. "On Generalized Lucas Pseudoprimality of Level k," Mathematics, MDPI, vol. 9(8), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:838-:d:534461
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