关于具有$k$的Pillai问题-广义斐波那契数和$2$的幂
On a problem of Pillai with $k$-generalised Fibonacci numbers and powers of $2$
摘要：
对于整数$ k\geq 2 $，设$ \{F^{(k)}_{n} \}_{n\geq 0}$是$ k$ -广义斐波那契序列，它以$ 0, \ldots, 0, 1 $（$ k $项）开始，其后的每一项是$ k $前面各项的和。在本文中，我们发现所有整数$c$至少有两个表示之间的差异$k$ -广义Fibonacci数和2的幂，任何固定的$k \geqslant 4$。本文推广了文献[9]中关于$k=2$情形和文献[6]中关于$k=3$情形的工作。
英文摘要：
For an integer $ k\geq 2 $, let $ \{F^{(k)}_{n} \}_{n\geq 0}$ be the $ k$--generalized Fibonacci sequence which starts with $ 0, \ldots, 0, 1 $ ($ k $ terms) and each term afterwards is the sum of the $ k $ preceding terms. In this paper, we find all integers $c$ having at least two representations as a difference between a $k$--generalized Fibonacci number and a powers of 2 for any fixed $k \geqslant 4$. This paper extends previous work from [9] for the case $k=2$ and [6] for the case $k=3$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
