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In this paper we consider the Diophantine equation $ V_n - b^m = c $ forgiven integers $ b,c $ with $ b \geq 2 $, whereas $ V_n $ varies amongLucas-Lehmer sequences of the second kind. We prove under some technicalconditions that if the considered equation has at least three solutions $ (n,m)$, then there is an upper bound on the size of the solutions as well as on thesize of the coefficients in the characteristic polynomial of $ V_n $.

On Pillai's Problem involving Lucas sequences of the second kind