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.
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The authors would like to thank the reviewers from the Online Encyclopedia of Integer Sequences for thoroughly checking, editing, reviewing, and finally approving the numerous new integer sequences introduced in this paper.
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Andrica, D., Bagdasar, O., Rassias, M.T. (2022). Weak Pseudoprimality Associated with the Generalized Lucas Sequences. In: Daras, N.J., Rassias, T.M. (eds) Approximation and Computation in Science and Engineering. Springer Optimization and Its Applications, vol 180. Springer, Cham. https://doi.org/10.1007/978-3-030-84122-5_4
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DOI: https://doi.org/10.1007/978-3-030-84122-5_4
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