J. V. Leyendekkers and A. G. Shannon

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

Volume 19, 2013, Number 2, Pages 49—59

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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

The structures of Fibonacci numbers, *F _{n}*, formed when n equals a prime, p, are analysed using the modular ring

*Z*

_{5}, Pascal’s Triangle as well as various properties of the Fibonacci numbers to calculate “Pascal-Fibonacci” numbers to test primality by demonstrating the many structural differences between the cases when

*F*is prime or composite.

_{n}### Keywords

- Fibonacci sequence
- Golden Ratio
- Modular rings
- Pascal’s triangle
- Binet formula

### AMS Classification

- 11B39
- 11B50

### References

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*Int. Journal of Mathematical Education in Science & Technology.*Vol. 44, 2013, No. 3, 350–364. - Kim, D. S., T. Kim, H. Y. Lee.
*p*-adic*q*-integral on*Z**p*associated with Frobenius-type Eulerian Polynomials and Umbral Calculus.*Advanced Studies in Contemporary Mathematics.*Vol. 23, 2013, No. 2, 243–251. - Knuth, D. E.
*Art of Computer Programming, Volume 4.*Addison-Wesley, New York, 2005, p. 50. - Leyendekkers, J. V., A. G. Shannon. The Structure of the Fibonacci Numbers in the Modular Ring
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## Related papers

## Cite this paper

APALeyendekkers, J. V., & Shannon, A. (2013). Fibonacci and Lucas primes. Notes on Number Theory and Discrete Mathematics, 19(2), 49-59.

ChicagoLeyendekkers, JV, and AG Shannon. “Fibonacci and Lucas Primes.” Notes on Number Theory and Discrete Mathematics 19, no. 2 (2013): 49-59.

MLALeyendekkers, Tieling, and AG Shannon. “Fibonacci and Lucas Primes.” Notes on Number Theory and Discrete Mathematics 19.2 (2013): 49-59. Print.