J. V. Leyendekkers and A. G. Shannon

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

Volume 22, 2016, Number 1, Pages 33–41

**Full paper (PDF, 206 Kb)**

## Details

### Authors and affiliations

J. V. Leyendekkers

*Faculty of Science, The University of Sydney, NSW 2006, Australia
*

A. G. Shannon

*Emeritus Professor, University of Technology Sydney, NSW 2007, Australia*

Campion College, PO Box 3052, Toongabbie East, NSW 2146, Australia

Campion College, PO Box 3052, Toongabbie East, NSW 2146, Australia

### Abstract

Various characteristics of the ordinary Fibonacci and Lucas sequences, many known for centuries, are shown to be common to generalized sequences related to the Golden Ratio. Periodicity properties are also investigated.

### Keywords

- Unit digits (right-end-digits)
- Modular rings
- Golden Ratio
- reduced Pythagorean triples
- Fibonacci and Lucas numbers
- Pythagorean triples

### AMS Classification

- 11B39
- 11B50

### References

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## Related papers

- Kosobutskyy, P. S. (2020). Phidias numbers as a basis for Fibonacci analogues.
*Notes on Number Theory and Discrete Mathematics*, 26(1), 172-178. - Nagaraja, K. M., & Dhanya, P. (2020). Identities on generalized Fibonacci and Lucas numbers.
*Notes on Number Theory and Discrete Mathematics*, 26 (3), 189-202.

## Cite this paper

Leyendekkers, J. V., & Shannon, A. G. (2016). Some Golden Ratio generalized Fibonacci and Lucas sequences. *Notes on Number Theory and Discrete Mathematics*, 22(1), 33-41.