  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.

Number Theory