<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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 pseudo-primes of level <italic>k</italic>, 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.</p>
</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 pseudo-primes 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.

On some links between the generalised Lucas pseudoprimes of level <italic>k</italic>

Department of Mathematics and Engineering Sciences

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On some links between the generalised Lucas pseudoprimes of level 

Pseudoprimes are composite integers sharing behaviours of the prime numbers, often used in practical applications like public-key cryptography. Many...

On some links between the generalised Lucas pseudoprimes of level k

Publié en ligne: 04 févr. 2023

Pages: 23 - 46

Reçu: 01 juil. 2022

Accepté: 30 sept. 2022

DOI: https://doi.org/10.2478/auom-2023-0002

Mots clés
Generalised Lucas sequences, Jacobi symbol, Pseudoprimality, Pseudoprimality of level

© 2023 Dorin Andrica et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On some links between the generalised Lucas pseudoprimes of level k

Publié en ligne: 04 févr. 2023

Pages: 23 - 46

Reçu: 01 juil. 2022

Accepté: 30 sept. 2022

DOI: https://doi.org/10.2478/auom-2023-0002

Mots clésGeneralised Lucas sequences, Jacobi symbol, Pseudoprimality, Pseudoprimality of level

© 2023 Dorin Andrica et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Generalised Lucas sequences, Jacobi symbol, Pseudoprimality, Pseudoprimality of level