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
A. Frigeri
2018-01-01
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 $\langlen \varphi \rangle +frac{1}{n}>1$.File in questo prodotto:
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