Nonnegative integer solutions of the equation L (k) n - L (k) m = 2 · 3a

For an integer k ≥ 2, let (L (k) n )n≥−(k−2) be the k-generalized Lucas sequence, which starts with 0, ..., 0, 2, 1 (k terms) and each term afterwards is the sum of the k preceding terms. In 2019, Bitim found all the solutions of the Diophantine equation Ln − Lm = 2 · 3 a . In this paper, we generalize this result by considering the k-generalized Lucas sequence, i.e., we solve the Diophantine equation L (k) n − L (k) m = 2 · 3 a in positive integers n, m, a with k ≥ 3. To obtain our main result, we use Baker’s method and the Baker-Davenport reduction method.