On some links between the generalised Lucas pseudoprimes of level k

Andrica, Dorin; Bagdasar, Ovidiu; Rassias, Michael Th.

doi:10.2478/auom-2023-0002

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.

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On some links between the generalised Lucas pseudoprimes of level k

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