J. V. Leyendekkers and A. G. Shannon

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 20, 2014, Number 2, Pages 6—9

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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

Fibonacci composites with prime subscripts, *F _{p}*, have factors (

*kp*± 1) in which

*k*is even. The class of

*p*governs the class of

*k*in the modular ring

*Z*

_{5}, and the digit sum of

*p*,

*F*and a function of

_{p}*F*provide an approximate check on primality.

_{p}### Keywords

- Fibonacci numbers
- Modular rings
- Digit sums
- Prime numbers
- Simson’s identity

### AMS Classification

- 11B39
- 11B50

### References

- Atanassov, K. T., A. G. Shannon. The Digital Root Function for Fibonacci-type Sequences.
*Advanced Studies in Contemporary Mathematics*. Vol. 21, 2011, No. 3, 251–254. - Gardiner, A. Digital Roots, Rings and Clock Arithmetic.
*The Mathematical Gazette*. Vol. 66 (437), 1982, 184–188. - 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. - Ribenboim, Paulo.
*My Numbers, My Friends: Popular Lectures on Number Theory*. Berlin, Springer-Verlag, 2000. - Shannon A. G., A. F. Horadam. Generalized staggered sums.
*The Fibonacci Quarterly*, Vol. 29, 1991, No. 1, 47–51.

## Related papers

## Cite this paper

APALeyendekkers, J., & Shannon, A. (2014). Fibonacci primes. Notes on Number Theory and Discrete Mathematics, 20(2), 6-9.

ChicagoLeyendekkers, JV, and AG Shannon. “Fibonacci Primes.” Notes on Number Theory and Discrete Mathematics 20, no. 2 (2014): 6-9.

MLALeyendekkers, JV, and AG Shannon. “Fibonacci Primes.” Notes on Number Theory and Discrete Mathematics 20.2 (2014): 6-9. Print.