Weak Pseudoprimality Associated with the Generalized Lucas Sequences
Book chapter
Andrica, D., Bagdasar, O. and Rassias, M.T. 2022. Weak Pseudoprimality Associated with the Generalized Lucas Sequences. in: Nicholas J. Daras and Themistocles M. Rassias (ed.) Approximation and Computation in Science and Engineering Springer. pp. 53-75
| Authors | Andrica, D., Bagdasar, O. and Rassias, M.T. |
|---|---|
| Editors | Nicholas J. Daras and Themistocles M. Rassias |
| 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. |
| Keywords | Generalized Bruckman–Lucas pseudoprime; Generalized Lucas sequence; Generalized Pell–Lucas sequence; Pseudoprime; Weak generalized Lucas pseudoprime; Weak generalized Bruckman–Lucas pseudoprime |
| Page range | 53-75 |
| Year | 2022 |
| Book title | Approximation and Computation in Science and Engineering |
| Publisher | Springer |
| Edition | 1 |
| Series | Springer Optimization and Its Applications |
| ISBN | 978-3-030-84122-5 |
| 978-3-030-84121-8 | |
| 978-3-030-84124-9 | |
| ISSN | 1931-6836 |
| Digital Object Identifier (DOI) | https://doi.org/10.1007/978-3-030-84122-5_4 |
| Web address (URL) | http://www.scopus.com/inward/record.url?eid=2-s2.0-85129740345&partnerID=MN8TOARS |
| Output status | Published |
| Publication dates | |
| Online | 05 May 2022 |
| Publication process dates | |
| Deposited | 25 May 2023 |
| Journal | Springer Optimization and Its Applications |
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Bagdasar, Ovidiu and Larcombe, Peter J. 2013. On the number of complex horadam sequences with a fixed period. Fibonacci Quarterly.On the characterization of periodic complex Horadam sequences
Bagdasar, Ovidiu and Larcombe, Peter J. 2013. On the characterization of periodic complex Horadam sequences. Fibonacci Quarterly.On a result of Bunder involving Horadam sequences: A proof and generalization
Larcombe, Peter J. and Bagdasar, Ovidiu 2013. On a result of Bunder involving Horadam sequences: A proof and generalization. Fibonacci Quarterly.Influence discovery in semantic networks: An initial approach
Trovati, M. and Bagdasar, O. 2014. Influence discovery in semantic networks: An initial approach. IEEE. https://doi.org/10.1109/uksim.2014.48Complementary iInequalities involving the Stolarsky Mean
Bagdasar, Ovidiu 2010. Complementary iInequalities involving the Stolarsky Mean. Journal of Inequalities and Applications. https://doi.org/10.1155/2010/492570Concise computer mathematics: tutorials on theory and problems
Bagdasar, Ovidiu 2013. Concise computer mathematics: tutorials on theory and problems. Springer.On the characterization of periodic generalized Horadam sequences
Bagdasar, Ovidiu and Larcombe, Peter J. 2014. On the characterization of periodic generalized Horadam sequences. Journal of Difference Equations and Applications. https://doi.org/10.1080/10236198.2014.891022Local maximum points of explicitly quasiconvex functions
Bagdasar, Ovidiu and Popovici, Nicolae 2014. Local maximum points of explicitly quasiconvex functions. Optimization Letters. https://doi.org/10.1007/s11590-014-0781-3A horadam-based pseudo-random number generator
Bagdasar, O.D., Chen, M. and Bagdasar, O. 2014. A horadam-based pseudo-random number generator. IEEE. https://doi.org/10.1109/uksim.2014.55On the structure of periodic complex Horadam orbits
Bagdasar, Ovidiu D., Larcombe, Peter J., Anjum, Ashiq and Bagdasar, O. 2016. On the structure of periodic complex Horadam orbits. Carpathian Journal of Mathematics.Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems
Popa, I.-L., Ceauşu, T., Bagdasar, O. and Agarwal, R.P. 2016. Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems. Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica. 27 (2), pp. 153-166. https://doi.org/10.2478/auom-2019-0025On some functions involving the lcm and gcd of integer tuples
Bagdasar, Ovidiu 2014. On some functions involving the lcm and gcd of integer tuples. Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics. https://doi.org/10.5937/SPSUNP1402091B