On Generalized Lucas Pseudoprimality of Level k

Dorin Andrica and Ovidiu Bagdasar
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Dorin Andrica: Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
Ovidiu Bagdasar: School of Computing and Engineering, University of Derby, Derby DE22 1GB, UK

Mathematics, 2021, vol. 9, issue 8, 1-17

Abstract: We investigate the Fibonacci pseudoprimes of level k , and we disprove a statement concerning the relationship between the sets of different levels, and also discuss a counterpart of this result for the Lucas pseudoprimes of level k . We then use some recent arithmetic properties of the generalized Lucas, and generalized Pell–Lucas sequences, to define some new types of pseudoprimes of levels k + and k ? and parameter a . For these novel pseudoprime sequences we investigate some basic properties and calculate numerous associated integer sequences which we have added to the Online Encyclopedia of Integer Sequences.

Keywords: generalized lucas sequences; legendre symbol; jacobi symbol; pseudoprimality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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