No abstract

p ℓ } be a finite set of primes and denote by U S the set of all rational integers whose prime factors are all in S. Let (U n ) n≥0 be a non-degenerate linear recurrence sequence with order at least two. In this paper, we study the finiteness result for the solutions of the Diophantine equationwhere n ≥ m and z 1 , . . . , z r ∈ U S . We also study the Diophantine equation U n + U m = wy q with w is a non-zero integer. In this case, we show that sum of two terms of recurrence sequence (U n ) n≥0 does not contain any q-th power if q is large enough.