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Fibonacci periods and multiples

Published online by Cambridge University Press:  08 February 2018

G. J. O. Jameson
G. J. O. Jameson*
Affiliation:
Dept. of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF e-mail: g.jameson@lancaster.ac.uk
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Extract

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. An easy induction verifies that F −n = (−1)n – 1Fn for n > 0.

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Type
Articles
Information
The Mathematical Gazette , Volume 102 , Issue 553 , March 2018 , pp. 63 - 76
Copyright
Copyright © Mathematical Association 2018 

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