On some links between the generalised Lucas pseudoprimes of level k

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.

Keywords

• generalised lucas sequences
• jacobi symbol
• pseudoprimality
• pseudoprimality of level k
• primary 11a51
• secondary 11b39, 11b50