Pell and Lucas primes

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 21, 2015, Number 3, Pages 64—69
Download full paper: PDF, 95 Kb

Details

Authors and affiliations

J. V. Leyendekkers
Faculty of Science, The University of Sydney
NSW 2006, Australia

A. G. Shannon
Faculty of Engineering & IT, University of Technology, Sydney
NSW 2007, Australia

Abstract

The structures of Pell and Lucas numbers, Pp and Lp with prime subscripts are compared in relation to the function (Kp ± 1) and for factors of the form (kp ± 1). It is found that digit sums give some guides to primality.

Keywords

  • Pell numbers
  • Lucas numbers
  • Primality
  • Digit sums

AMS Classification

  • 11B39
  • 11B50

References

  1. Dubner, H., & Keller, W. (1999) New Fibonacci and Lucas Primes. Mathematics of Computation. 68, 417−427.
  2. Forget, T. W., & Larkin, T. A. (1968). Pythagorean Triads of the form x, x + 1, z described by Recurrence Sequences. The Fibonacci Quarterly 6 (3): 94–104.
  3. Horadam, A.F. (1971) Pell Identities. The Fibonacci Quarterly. 9 (3): 245–252, 263.
  4. Leyendekkers, J. V., & Shannon, A. G. (1998) Fibonacci Numbers within Modular Rings. Notes on Number Theory and Discrete Mathematics. 4 (4): 165–174.
  5. Leyendekkers, J. V., & Shannon, A. G. (2013) The Structure of the Fibonacci Numbers in the Modular Ring Z5. Notes on Number Theory and Discrete Mathematics. 19(1), 66–72.
  6. Leyendekkers, J. V., & Shannon, A. G. (2013) Fibonacci and Lucas Primes. Notes on Number Theory and Discrete Mathematics. 19(2): 49–59.
  7. Leyendekkers, J. V., & Shannon, A. G. (2014) Fibonacci Primes. Notes on Number Theory and Discrete Mathematics. 20(2), 6–9.
  8. Leyendekkers, J. V., & Shannon, A. G. (2014) Fibonacci Numbers with Prime Subscripts: Digital Sums for Primes versus Composites. Notes on Number Theory and Discrete Mathematics. 20(3), 45–49.
  9. Leyendekkers, J. V., & Shannon, A. G. (2014) Fibonacci Number Sums as Prime Indicators. Notes on Number Theory and Discrete Mathematics, 20(4), 47–52.
  10. Leyendekkers, J. V., Shannon, A. G. & Rybak, J.M. (2007) Pattern Recognition: Modular Rings and Integer Structure. North Sydney: Raffles KvB Monograph No.9.
  11. McDaniel, W. (2002) On Fibonacci and Pell Numbers of the form kx2: Almost every term has a 4r + 1 prime factor. The Fibonacci Quarterly. 40(1), 41–42.
  12. Ray, P. K. (2013) New Identities for the Common Factors of Balancing and Lucas-Balancing numbers. Int. J. of Pure and Applied Mathematics. 85(3), 487–494.
  13. Ribenboim, P. (1999) Pell Numbers, Squares and Cubes. Publicationes Mathematicae-Debrecen. 54(1–2), 131–152.
  14. Robbins, N. (1983) On Fibonacci Numbers of the Form PX2 where P is Prime. The Fibonacci Quarterly. 21(3), 266–271.
  15. Robbins, N. (1984) On Pell Numbers of the Form PX2 where P is Prime. The Fibonacci Quarterly. 22(4), 340–348.
  16. Watkins, J J. (2014) Number Theory: A Historical Approach. Princeton and Oxford: Princeton University Press, pp. 271–272.

Related papers

Cite this paper

APA

Leyendekkers, J. V., & Shannon, A. G. (2015). Pell and Lucas primes. Notes on Number Theory and Discrete Mathematics, 21(3), 64-69.

Chicago

Leyendekkers, J. V., and A. G. Shannon. “Pell and Lucas Primes.” Notes on Number Theory and Discrete Mathematics 21, no. 3 (2015): 64-69.

MLA

Leyendekkers, J. V., and A. G. Shannon. “Pell and Lucas Primes.” Notes on Number Theory and Discrete Mathematics 21.3 (2015): 64-69. Print.

Comments are closed.