Fibonacci periods and multiples

The well-known Fibonacci numbers Fn are defined by the recurrence relation Fn = F n – 1 + F n – 2. (1) together with the starting values F 0 = 0, F 1 = 1, or equivalently F 1 = F 2 = 1. We record the first few: The recurrence relation can also be applied backwards in the form Fn = F n + 2 – F n + 1 to define Fn for n 0.