On a problem of Pillai with Fibonacci numbers and powers of 3.

Abstract

Consider the sequence ${\left\{F_n\right\}}_{n\ge 0}$ of Fibonacci numbers defined by $F_0=0$ , $F_1=1$ , and $F_{n+2}=F_{n+1}+F_n$ for all $n\ge 0$ . In this paper, we find all integers c having at least two representations as a difference between a Fibonacci number and a power of 3.