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

Consider the sequence { F n } n ≥ 0 of Fibonacci numbers defined by F 0 = 0 , F 1 = 1 , and F n + 2 = F n + 1 + F n for all n ≥ 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.