J. V. Leyendekkers and A. G. Shannon

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

Volume 10, 2004, Number 1, Pages 12—23

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## Details

### Authors and affiliations

J. V. Leyendekkers

*The University of Sydney, 2006 Australia*

A. G. Shannon

*Warrane College, Kensington, NSW 1465,
& KvB Institute of Technology, North Sydney, NSW 2060, Australia *

### Abstract

An analysis is made of the class and row structures of Fibonacci numbers within the modular ring Z_{4}. It is found that the class structure repeats the pattern ̅0_{4} ̅1_{4} ̅1_{4} ̅2_{4} ̅3_{4} ̅1_{4}. Two thirds of the rows in the ring array are even and all are a sum of Fibonacci numbers. Sums of Fibonacci numbers, covering ten, five and three consecutive numbers or number types, had factors of 11, 11 × 31, or 101; (these include specific sets). The Fibonacci number primes all belong to the Class ̅1_{4} and therefore equal a sum of squares. There is only one unique set of squares with no common factors. The factors found for the sums have a link with Fermat and Mersenne numbers.

### AMS Classification

- 06F25
- 11B39

### References

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## Cite this paper

Leyendekkers, J. V., and Shannon, A. G. (2004). The structure of Fibonacci numbers in modular rings. Notes on Number Theory and Discrete Mathematics, 10(1), 12-23.