On some links between the generalised Lucas pseudoprimes of level k

Journal article

Andrica, Dorin, Bagdasar, O. and Rassias, Michael Th. 2023. On some links between the generalised Lucas pseudoprimes of level k. Analele Universitatii "Ovidius" Constanta - Seria Matematica. Vol 31 (Issue 1), pp. 23-46. https://doi.org/10.2478/auom-2023-0002
AuthorsAndrica, Dorin, Bagdasar, O. and Rassias, Michael Th.
Abstract

Pseudoprimes are composite integers sharing behaviours of the prime numbers, often used in practical applications like public-key cryptography. Many pseudoprimality notions known in the literature are defined by recurrent sequences. In this paper we first establish new arithmetic properties of the generalized Lucas and Pell-Lucas sequences. Then we study the recent notion of generalized Pell and Pell-Lucas pseudoprimes of level k, and find inclusions between the sets of pseudoprimes on different levels. In this process we extend several results concerning Fibonacci, Lucas, Pell, and Pell-Lucas sequences.

KeywordsGeneralised Lucas sequences; Jacobi symbol; Pseudoprimality; Pseudoprimality of level k
Year2023
JournalAnalele Universitatii "Ovidius" Constanta - Seria Matematica
Journal citationVol 31 (Issue 1), pp. 23-46
PublisherOVIDIUS UNIV PRESS
Sciendo
ISSN1844-0835
1224-1784
Digital Object Identifier (DOI)https://doi.org/10.2478/auom-2023-0002
Web address (URL)https://sciendo.com/article/10.2478/auom-2023-0002
https://publons.com/wos-op/publon/58031760/
https://www.scopus.com/record/display.uri?eid=2-s2.0-85147886590&origin=resultslist&sort=plf-f&src=s&st1=On+some+links+between+the+generalised+Lucas+pseudoprimes+of+level+k&sid=d305c19eba8dfee7d7def720d1cd8590&sot=b&sdt=b&sl=82&s=TITLE-ABS-KEY%28On+some+links+between+the+generalised+Lucas+pseudoprimes+of+level+k%29&relpos=0&citeCnt=0&searchTerm=
Output statusPublished
Publication dates01 Jan 2023
Online04 Feb 2023
Publication process dates
Accepted30 Sep 2022
Deposited25 May 2023
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Bagdasar, O. and Andrica, D. 2017. New results and conjectures on 2-partitions of multisets. 7th International Conference on Modeling, Simulation, and Applied Optimization, ICMSAO 2017. IEEE Computer Society. https://doi.org/10.1109/icmsao.2017.7934928
ON THE MASKED PERIODICITY OF HORADAM SEQUENCES: A GENERATOR-BASED APPROACH
Bagdasar, Ovidiu D., Larcombe, Peter J. and Bagdasar, O. 2017. ON THE MASKED PERIODICITY OF HORADAM SEQUENCES: A GENERATOR-BASED APPROACH. Fibonacci Quarterly.
LOCAL MAXIMIZERS OF GENERALIZED CONVEX VECTOR-VALUED FUNCTIONS
Bagdasar, Ovidiu, Popovici, Nicolae and Bagdasar, O. 2017. LOCAL MAXIMIZERS OF GENERALIZED CONVEX VECTOR-VALUED FUNCTIONS. Journal of Nonlinear and Convex Analysis.
On the number of complex horadam sequences with a fixed period
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.2014.48
Complementary iInequalities involving the Stolarsky Mean
Bagdasar, Ovidiu 2010. Complementary iInequalities involving the Stolarsky Mean. Journal of Inequalities and Applications. https://doi.org/10.1155/2010/492570
Concise 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/10.1080/10236198.2014.891022
Local 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/s11590-014-0781-3
A 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.2014.55
On 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-2019-0025
On 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
ON A RESULT OF BUNDER INVOLVING HORADAM SEQUENCES: A NEW PROOF
Larcombe, Peter J., Bagdasar, O. and Fennessey, Eric J. 2014. ON A RESULT OF BUNDER INVOLVING HORADAM SEQUENCES: A NEW PROOF. Fibonacci Quarterly. pp. 175-177.