K. T. Atanassov, R. D. Knott, R. L. Ollerton and A. G. Shannon

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

Volume 12, 2006, Number 2, Pages 13—20

**Download full paper: PDF, 58 Kb**

## Details

### Authors and affiliations

K. T. Atanassov

*Centre for Biomedical Engineering, Bulgarian Academy of Sciences,
Sofia-1113, Bulgaria
*

R. D. Knott

*92 Pennine Road, Horwich,
Bolton, BL6 7HW, United Kingdom
*

R. L. Ollerton

*University of Western Sydney, Penrith Campus DC1797, Australia*

A. G. Shannon

*Warrane College, The University of New South Wales, 1465 &
KvB Institute of Technology, North Sydney, NSW, 2060, Australia
*

### Abstract

This paper continues our study of Fibonacci inequalities. For the set *A _{n}* = {

*F*

_{n−1}, 4

*F*

_{n−2}, …, (

*n*−2)

^{2}

*F*

_{2}} with

*k*

^{th}element given by

*a*=

_{k}*k*

^{2}

*F*, it is proved that the unique maximal element is given by

_{n−k}*a** =

*a*

_{4}= 16

*F*

_{n−4},

*n*≥ 9.

### AMS Classification

- 11B39

### References

- K.T. Atanassov, Ron Knott, Kiyota Ozeki, A.G. Shannon, László Szalay. “Inequalities Among Related Pairs of Fibonacci Numbers.”
*The Fibonacci Quarterly*. 41 (2003):20-22. - S. Vajda,
*Fibonacci and Lucas Numbers and the Golden Section: Theory and Applications*. Chichester: Ellis Horwood, 1989. - N. Gauthier, “Two Fibonacci Sums – a Variation.”
*Mathematical Gazette*. 81 (1997): 85-88. - P. Glaister. “Fibonacci Sums of the Type .”
*Mathematical Gazette*. 79 (1995): 364-367. - A.F. Horadam. “Basic Properties of a Certain Generalized Sequence of Numbers.”
*The Fibonacci Quarterly*. 3 (1965): 161-176. - Wolfram Research Inc http://mathworld.wolfram.com/FibonacciNumber.html.
- Kiyota Ozeki, “On Weighted Fibonacci and Lucas Sums.”
*The Fibonacci Quarterly*, 43 (2005): 104-107.

## Related papers

## Cite this paper

APAAtanassov, K. T., Knot, R. D., Ollerton, R. L., & Shannon, A. G. (2006). An extremal problem related to the Fibonacci sequence. Notes on Number Theory and Discrete Mathematics, 12(2), 13-20.

ChicagoAtanassov, K. T., R. D. Knott, R. L. Ollerton, and A. G. Shannon. “An Extremal Problem Related to the Fibonacci Sequence.” Notes on Number Theory and Discrete Mathematics 12, no. 2 (2006): 13-20.

MLAAtanassov, K. T., R. D. Knott, R. L. Ollerton, and A. G. Shannon. “An Extremal Problem Related to the Fibonacci Sequence.” Notes on Number Theory and Discrete Mathematics 12.2 (2006): 13-20. Print.