For an integer [Formula: see text], let [Formula: see text] be the [Formula: see text]-generalized Fibonacci sequence which starts with [Formula: see text] (a total of [Formula: see text] terms) and for which each term afterwards is the sum of the [Formula: see text] preceding terms. In this paper, we find all integers [Formula: see text] with at least two representations as a difference between a [Formula: see text]-generalized Fibonacci number and a power of [Formula: see text]. This paper continues the previous work of the first author for the Fibonacci numbers, and for the Tribonacci numbers.

中文翻译：

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关于具有 k-广义斐波那契数和 3 次方的 Pillai 问题

对于整数 [Formula: see text]，令 [Formula: see text] 为 [Formula: see text]-以 [Formula: see text] 开头的广义斐波那契数列（总共 [Formula: see text] 项）并且之后的每个术语都是[公式：参见文本]前面的术语的总和。在本文中，我们发现所有整数 [公式：参见文本] 至少具有两种表示形式，作为 [公式：参见文本] 广义斐波那契数与 [公式：参见文本] 的幂之间的差异。本文延续了第一作者之前关于斐波那契数和 Tribonacci 数的工作。