Pseudoprimality related to the generalized Lucas sequences

Abstract Some arithmetic properties and new pseudoprimality results concerning generalized Lucas sequences are presented. The findings are connected to the classical Fibonacci, Lucas, Pell, and Pell-Lucas pseudoprimality. During the process new integer sequences are found and some conjectures are formulated.

[1]  P. Ribenboim.  The Little Book of Bigger Primes , 2004 .

[2]  J. H. Jaroma.  Note on the Lucas-Lehmer Test , 2004, Irish Mathematical Society Bulletin.

[3]  A. Rotkiewicz.  LUCAS AND FROBENIUS PSEUDOPRIMES , 2003 .

[4]  C. Pomerance,et al.  Prime Numbers: A Computational Perspective , 2002 .

[5]  D. H. Lehmer,et al.  New primality criteria and factorizations of 2^{}±1 , 1975 .

[6]  Robert Baillie,et al.  Lucas Pseudoprimes , 2002 .

[7]  Dorin Andrica,et al.  On Some New Arithmetic Properties of the Generalized Lucas Sequences , 2021, Mediterranean Journal of Mathematics.

[8]  S. Paul.  ON THE INFINITUDE OF LUCAS PSEUDOPRIMES , 1994 .

[9]  H. C. Williams,et al.  Édouard Lucas and primality testing , 1999 .

[10]  Elias M. Stein,et al.  Models of degenerate Fourier integral operators and Radon transforms , 1994 .

[11]  C. Pomerance,et al.  There are infinitely many Carmichael numbers , 1994 .

[12]  N. J. A. Sloane,et al.  The On-Line Encyclopedia of Integer Sequences , 2003, Electron. J. Comb..

[13]  Jon Grantham,et al.  Frobenius pseudoprimes , 2001, Math. Comput..

[14]  A. F. Horadam,et al.  ON LUCAS PSEUDOPRIMES WHICH ARE PRODUCTS OF S PRIMES , 2007 .

[15]  F. Al-Thukair,et al.  On Fibonacci and Lucas sequences modulo a prime and primality testing , 2018 .

[16]  Thomas Koshy,et al.  Fibonacci and Lucas Numbers With Applications , 2018 .

[17]  S. Schuster,et al.  Use of Fibonacci numbers in lipidomics – Enumerating various classes of fatty acids , 2017, Scientific Reports.

[18]  Eric L. Roettger,et al.  A search for Fibonacci-Wieferich and Wolstenholme primes , 2007, Math. Comput..

[19]  Karl Dilcher,et al.  A search for Wieferich and Wilson primes , 1997, Math. Comput..

[20]  Jon Grantham.  There are infinitely many Perrin pseudoprimes , 2010, 1903.06825.

[21]  E. Wright,et al.  An Introduction to the Theory of Numbers , 1939 .

[22]  T. Andreescu,et al.  Number Theory: Structures, Examples, and Problems , 2009 .