Fibonacci and Lucas Identities the Golden Way

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.

16 pages, no figures, no tables

References in corpus (1)

• Weighted sums of some second-order sequences