On k-Fibonacci and k-Lucas numbers written as a product of two Pell numbers

Let k >= 2. A generalization of the well-known Fibonacci and Lucas sequences are the k-Fibonacci and k-Lucas sequences. For these sequences, the first k terms are0,...,0,1 and 0,...,0,2,1, respectively, and each term afterwards is the sum of the preceding k terms. The principal objective of this manuscript is to identify all instances of k-Fibonacci and k-Lucas numbers that can be expressed as the product of two Pell numbers. This generalizes the result from Ref. Ddamulira et al.(Fibonacci Q 54: 11-18, 2016).