Number Theory

   

A New Formula for the Sum of the Sixth Powers of Fibonacci Numbers

Authors: Hideyuki Ohtsuka, Shigeru Nakamura

Sloane's On-Line Encyclopedia of Integer Sequences incorrectly states a lengthy formula for the sum of the sixth powers of the first n Fibonacci numbers. In this paper we prove a more succinct formulation. We also provide an analogue for the Lucas numbers. Finally, we prove a divisibility result for the sum of certain even powers of the first n Fibonacci numbers.

Comments: 3 Pages, Published: Congressus Numerantum, Proceedings of the Thirteenth Conference on Fibonacci Numbers and their Applications, Vol. 201, pp.297-300 (2010).

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Submission history

[v1] 9 Oct 2009

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