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
Download full paper: PDF, 89 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
Fibonacci composites with prime subscripts, Fp, have factors (kp ± 1) in which k is even. The class of p governs the class of k in the modular ring Z5, and the digit sum of p, Fp and a function of Fp provide an approximate check on primality.
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
Leyendekkers, J., & Shannon, A. (2014). Fibonacci primes. Notes on Number Theory and Discrete Mathematics, 20(2), 6-9.