The Distribution of Self-Fibonacci Divisors

20 Feb 2015 · Luca Florian, Tron Emanuele ·

Consider the positive integers $n$ such that $n$ divides the $n$-th Fibonacci number, and their counting function $A$. We prove that \[A(x) \leq x^{1-(1/2+o(1))\log\log\log x/\log\log x}.\]