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LetA ∈ N,B ∈ Z with gcd (A,B) = 1 ,B(∈/){ - 1,0,1 }. For the binary recurrence (Lucas se-quence) of the form u0 = 0, u1 = 1 , un+2 = Aun+1 + Bun, let N1 (A,B,k) be the number of the terms n of | un= k, where k ∈ N. In this paper, using a new result of Bil