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arXiv · 1810.12115

Fibonacci and Lucas Identities the Golden Way

Kunle Adegoke
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Abstract

By expressing Fibonacci and Lucas numbers in terms of the powers of the golden ratio, $\alpha=(1+\sqrt 5)/2$ and its inverse, $\beta=-1/\alpha=(1-\sqrt 5)/2$, a multitude of Fibonacci and Lucas identities have been developed in the literature. In this paper, we follow the reverse course: we derive numerous Fibonacci and Lucas identities by making use of the well-known expressions for the powers of $\alpha$ and $\beta$ in terms of Fibonacci and Lucas numbers.

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Kunle Adegoke. 2018-10-25. Fibonacci and Lucas Identities the Golden Way. https://arxiv.org/abs/1810.12115

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