On a variant of Pillai's problem involving S -units and Fibonacci numbers.

Let us denote by F n the n -th Fibonacci number. In this paper we show that there exist at most finitely many integers c such that the exponential Diophantine equation F n - 2 x 3 y = c has more than one solution ( n , x , y ) ∈ N 3 with n > 1 . Moreover, in the case that c > 0 we find all integers c such that the Diophantine equation has at least three solutions and in the case that c < 0 we find all integers c such that the Diophantine equation has at least four solutions.