On the greatest common divisor of $n$ and the $n$th Fibonacci number

Paolo Leonetti, Carlo Sanna

Let $\mathcal{A}$ be the set of all integers of the form $\gcd (n,F_n)$, where $n$ is a positive integer and $F_n$ denotes the $n$th Fibonacci number. We prove that $\#\left(\mathc…