Fibonacci periods and multiples

Abstract

The well-known Fibonacci numbers Fn are defined by the recurrence relationFn = Fn – 1 + Fn – 2. (1)together with the starting values F0 = 0, F1 = 1, or equivalently F1 = F2 = 1.We record the first few:The recurrence relation can also be applied backwards in the form Fn = Fn + 2 – Fn + 1 to define Fn for n < 0. An easy induction verifies that F−n = (−1)n – 1Fn for n > 0.