English

A note on Fibonacci number of even index

Number Theory 2017-06-14 v2

Abstract

We prove that a positive integer nn is a Fibonacci number of even index if and only if nφ+1n>1\langle n\varphi\rangle+\frac{1}{n}>1.

Keywords

Cite

@article{arxiv.1705.08305,
  title  = {A note on Fibonacci number of even index},
  author = {Achille Frigeri},
  journal= {arXiv preprint arXiv:1705.08305},
  year   = {2017}
}

Comments

5 pages There is an error in the main proof (cases 3 and 5). Uniqueness for the decomposition of Fibonacci number of even index is not proved