We introduce a representation of the integers based only on Fibonacci numbers of odd index. Then we give an elementary combinatorial proof of the fact that a positive integer n is a Fibonacci number of even index if and only $\langlen \varphi \rangle +frac{1}{n}>1$.

A Note on Fibonacci Numbers of Even Index

Abstract

We introduce a representation of the integers based only on Fibonacci numbers of odd index. Then we give an elementary combinatorial proof of the fact that a positive integer n is a Fibonacci number of even index if and only $\langlen \varphi \rangle +frac{1}{n}>1$.
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Fibonacci numbers
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1086908