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

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## 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

Sums of the first *p* Fibonacci numbers, *S _{p}*, are shown to be related to

*K*in

*F*=

_{p}*Kp*± 1, which is itself a useful indicator of primality for

*F*. Digit sums of

_{p}*K*,

*S*, sums of

_{p}*F*

_{p}^{2}and Simson’s identity were compared.

### Keywords

- Fibonacci numbers
- Primality
- Digit sums

### AMS Classification

- 11B39
- 11B50

### References

- Fujiwara, M., Y. Ogawa. Introduction to Truly Beautiful Mathematics. Tokyo: Chikuma Shobo, 2005.
- 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.
- Leyendekkers, J. V., A. G. Shannon. Fibonacci and Lucas Primes. Notes on Number Theory and Discrete Mathematics, Vol. 19, 2013, No. 2, 49–59.
- Leyendekkers, J. V., A. G. Shannon. The Pascal–Fibonacci Numbers. Notes on Number Theory and Discrete Mathematics. Vol. 19, 2013, No. 3, 5–11.
- 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.
- Leyendekkers, J. V., A. G. Shannon. Fibonacci Primes. Notes on Number Theory and Discrete Mathematics. Vol. 20, 2014, No. 2, 6–9.
- 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.
- Shallit, J. O. On Infinite Products Associated with Sums of Digits. Journal of Number Theory. Vol. 21, 1985, No. 2, 128–134.
- Watkins, J. J. Number Theory: A Historical Approach. Princeton and Oxford: Princeton University Press, 2014, 271–272.

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## Cite this paper

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

ChicagoLeyendekkers, J. V., and A. G. Shannon. “Fibonacci Number Sums as Prime Indicators.” Notes on Number Theory and Discrete Mathematics 20, no. 4 (2014): 47-52.

MLALeyendekkers, J. V., and A. G. Shannon. “Fibonacci Number Sums as Prime Indicators.” Notes on Number Theory and Discrete Mathematics 20.4 (2014): 47-52. Print.