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

Mahadi Ddamulira

Published 2019-02-09Version 1

Consider the sequence $ \{F_{n}\}_{n\geq 0} $ of Fibonacci numbers defined by $ F_0=0 $, $ F_1 =1$ and $ F_{n+2}=F_{n+1}+ F_{n} $ for all $ n\geq 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 $.