Let \(k\ge 2\). A generalization of the well-known Fibonacci sequence is the k-Fibonacci sequence. For this sequence, the first k terms are \(0,\ldots ,0,1\) and each term afterwards is the sum of the preceding k terms. In this paper, we find all k-Fibonacci which are product of two Fermat numbers.

中文翻译：

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k-Fibonacci 数与两个费马数的乘积之间的重合

让\(k\ge 2\)。众所周知的斐波那契数列的推广是k -斐波那契数列。对于这个序列，前k项是\(0,\ldots ,0,1\)，之后的每一项都是前面k项的总和。在本文中，我们找到所有k -Fibonacci，它们是两个费马数的乘积。