Fibonacci number sums as prime indicators

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 20, 2014, Number 4, Pages 47–52
Full paper (PDF, 136 Kb)

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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

Sums of the first p Fibonacci numbers, Sp, are shown to be related to K in Fp = Kp ± 1, which is itself a useful indicator of primality for Fp. Digit sums of K, Sp, sums of Fp2 and Simson’s identity were compared.

Keywords

  • Fibonacci numbers
  • Primality
  • Digit sums

AMS Classification

  • 11B39
  • 11B50

References

  1. Fujiwara, M., Y. Ogawa. Introduction to Truly Beautiful Mathematics. Tokyo: Chikuma Shobo, 2005.
  2. Grabner, P. J., T. Herendi, R. F. Tichy. Fractal Digital Sums and Codes. Applicable Algebra in Engineering, Communication and Computing, Vol. 8, 1997, No. 1, 33–39.
  3. Leyendekkers, J. V., A. G. Shannon. Fibonacci and Lucas Primes. Notes on Number Theory and Discrete Mathematics, Vol. 19, 2013, No. 2, 49–59.
  4. Leyendekkers, J. V., A. G. Shannon. The Pascal–Fibonacci Numbers. Notes on Number Theory and Discrete Mathematics. Vol. 19, 2013, No. 3, 5–11.
  5. Leyendekkers, J. V., A. G. Shannon. The Decimal String of the Golden Ratio. Notes on Number Theory and Discrete Mathematics. Vol. 20, 2014, No. 1, 27–31.
  6. Leyendekkers, J. V., A. G. Shannon. Fibonacci Primes. Notes on Number Theory and Discrete Mathematics. Vol. 20, 2014, No. 2, 6–9.
  7. Leyendekkers, J. V., A. G. Shannon. Fibonacci Numbers with Prime Subscripts: Digital Sums for Primes versus Composites. Notes on Number Theory and Discrete Mathematics, Vol. 20, 2014, No. 3, 45–49.
  8. Shallit, J. O. On Infinite Products Associated with Sums of Digits. Journal of Number Theory. Vol. 21, 1985, No. 2, 128–134.
  9. Watkins, J. J. Number Theory: A Historical Approach. Princeton and Oxford: Princeton University Press, 2014, 271–272.

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Cite this paper

Leyendekkers, J. V., & Shannon, A. G. (2014). Fibonacci number sums as prime indicators. Notes on Number Theory and Discrete Mathematics, 20(4), 47-52.

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