Robert Frontczak

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 24, 2018, Number 2, Pages 94—103

DOI: 10.7546/nntdm.2018.24.2.94-103

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## Details

### Authors and affiliations

Robert Frontczak

*Landesbank Baden-Wuerttemberg
Am Hauptbahnhof 2, 70173 Stuttgart, Germany*

### Abstract

We derive expressions for sums of first, second, third and fourth powers of Fibonacci and Lucas numbers and their alternating versions. On our way of exploration we rediscover some known results and present new. Focusing on third and fourth order power sums, our findings complete those of Clary and Hemenway, Melham and Adegoke.

### Keywords

- Fibonacci number
- Lucas number
- Sums of powers

### 2010 Mathematics Subject Classification

- 11B37
- 11B39

### References

- Adegoke, K., Sums of fourth powers of Fibonacci and Lucas numbers, Preprint, May 2017, Available via arXiv.
- Adegoke, K., Factored closed-form expressions for the sums of cubes of Fibonacci and Lucas numbers, Preprint, June 2017, Available via arXiv.
- Clary, S. & Hemenway, P. D. (1993) On sums of cubes of Fibonacci numbers, in Applications of Fibonacci Numbers, Kluwer Academic Publishers, 123–136.
- Daykin, D. E. & Dresel, L. A. G. (1967) Identities for products of Fibonacci and Lucas numbers, The Fibonacci Quarterly, 5 (4), 367–370.
- Kilic, E., Omur, N. & Ulutas, Y. (2011) Alternating sums of the powers of Fibonacci and Lucas numbers, Miskolc Mathematical Notes, 12 (1), 87–103.
- Melham, R.S. (2000) Alternating sums of fourth powers of Fibonacci and Lucas numbers, The Fibonacci Quarterly, 38 (3), 254–259.

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## Cite this paper

APAFrontczak, R. (2018). Sums of powers of Fibonacci and Lucas numbers: A new bottom-up approach. Notes on Number Theory and Discrete Mathematics, 24(2), 94-103, doi: 10.7546/nntdm.2018.24.2.94-103.

ChicagoFrontczak, Robert. “Sums of Powers of Fibonacci and Lucas Numbers: A New Bottom-up Approach.” Notes on Number Theory and Discrete Mathematics 24, no. 2 (2018): 94-103, doi: 10.7546/nntdm.2018.24.2.94-103.

MLAFrontczak, Robert. “Sums of Powers of Fibonacci and Lucas Numbers: A New Bottom-up Approach.” Notes on Number Theory and Discrete Mathematics 24.2 (2018): 94-103. Print, doi: 10.7546/nntdm.2018.24.2.94-103.