On a variant of Pillai's problem II
  In this paper, we show that there are only finitely many $c$ such that the equation $U_n - V_m = c$ has at least two distinct solutions $(n,m)$, where $\{U_n\}_{n\geq 0}$ and $\{V_m\}_{m\geq 0}$ are given linear recurrence sequences. 
Kwok Chi Chim and Istv\'an Pink and Volker Ziegler
math.NT