On Palindromic forms in the k-Lucas sequence composed of two distinct Repdigits

For integers k ≥ 2, the k-generalized Lucas sequence ₙ⁽ᵏ⁾ ≥ 2-k is defined by the recurrence relation \[ L_n⁽ᵏ⁾ = Lₙ₋₁⁽ᵏ⁾ + ⋯ + Lₙ₋ₖ⁽ᵏ⁾ for n ≥ 2, \] with initial terms given by L₀⁽ᵏ⁾ = 2, L₁⁽ᵏ⁾ = 1, and L₂₋ₖ⁽ᵏ⁾ = ⋯ = L₋₁⁽ᵏ⁾ = 0. In this paper, we extend work in {Lucas} and show that the result in {Lucas} still holds for k≥ 3, that is, we show that for k≥ 3, there is no k-generalized Lucas number appearing as a palindrome formed by concatenating two distinct repdigits.