Can a k-Lucas Number be a Product of Two Fermat Numbers?

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发表日期：

2024年

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Alioune Gueye,
Salah Eddine Rihane,
Alain Togbé

摘要

Let \(k\ge 2\) . A generalization of the well-known Lucas sequence is the k-Lucas sequences. For this sequence, the first k terms are \(0,\ldots ,0,2,1\) and each term afterwards is the sum of the preceding k terms. In this paper, we show that there is no k-Lucas written as product of two Fermat numbers.