k-Fibonacci and k-Lucas Numbers as Product of Two Repdigits

Let k >= 2. A generalization of the well-known Fibonacci and Lucas sequences are the k-Fibonacci and k-Lucas sequences, respectively. For these sequences the first k terms are 0, ... , 0,1 and 0, ... , 0, 2, 1, respectively, and each term afterwards is the sum of the preceding k terms. In this manuscript, our main objective is to find all k-Fibonacci and k-Lucas numbers which are product of two repdigits. This generalizes the result from Erduvan and Keskin (Turk J Math 43: 2142-2153, 2019).