Abstract
Let \(k\ge 2\). 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 are \(0,\ldots ,0,1\) and \(0,\ldots ,0,2,1\), 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).
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Rihane, S.E. On k-Fibonacci and k-Lucas numbers written as a product of two Pell numbers. Bol. Soc. Mat. Mex. 30, 20 (2024). https://doi.org/10.1007/s40590-024-00593-9
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DOI: https://doi.org/10.1007/s40590-024-00593-9