Is there anywhere an elegant proof that Phi**n = F(n-1) + [F(n) * Phi]
where F(x) is the value of the Fibonacci number x and Phi is the "Golden
ratio" defined as Phi**2 - Phi - 1 = 0. I can demonstrate it with ease
for an arbitrary value of n, but I seem to have forgotten the proof for
all values of n. (BTW ** is the standard "raise to the power of"]

A virtual bottle of your alcoholic liquid of choice to the poster of the
most elegant proof.

The judge's decision is final and lots of correspondence will be entered
into.

John

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