The Distribution of Self-Fibonacci Divisors

Abstract

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

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