English

The Distribution of Self-Fibonacci Divisors

Number Theory 2015-02-23 v2

Abstract

Consider the positive integers nn such that nn divides the nn-th Fibonacci number, and their counting function AA. We prove that A(x)x1(1/2+o(1))logloglogx/loglogx.A(x) \leq x^{1-(1/2+o(1))\log\log\log x/\log\log x}.

Keywords

Cite

@article{arxiv.1410.2489,
  title  = {The Distribution of Self-Fibonacci Divisors},
  author = {Florian Luca and Emanuele Tron},
  journal= {arXiv preprint arXiv:1410.2489},
  year   = {2015}
}

Comments

8 pages. 1/4 improved to 1/2. To appear in the proceedings of CNTA XIII