论文标题
在非平凡的小除数和大型除数中，最多两次的秩序线性复发
Linear recurrences of order at most two in nontrivial small divisors and large divisors
论文作者
论文摘要
对于每个积极整数$ n $，定义$$ s'_n \ = \ {1 <d <d <\ sqrt {n}：d | n \} \ mbox {and} l'_n _n \ = \ \ \ \ \ \ \ \ \ \ \ \ \ {\ sqrt {\ sqrt {n}一组小除数$ \ {d \ le \ sqrt {n}：d | n \} $最多满足订单的线性复发。我们通过从考虑中排除了琐碎的除数$ 1 $，从而非微不足道地扩展了结果，从而大大提高了分析的复杂性。我们的第一个结果是所有正整数$ n $的特征，使得$ s'_n $最多满足订单的线性复发。此外，我们的第二个结果是所有正$ n $的特征，使得$ l'_n $最多满足订单的线性复发，从而扩展了最近的结果，其表征$ n $，$ l'_n $处于算术上。
For each positive integer $N$, define $$S'_N \ =\ \{1 < d < \sqrt{N}: d|N\}\mbox{ and }L'_N \ =\ \{\sqrt{N} < d < N : d|N\}.$$ Recently, Chentouf characterized all positive integers $N$ such that the set of small divisors $\{d\le \sqrt{N}: d|N\}$ satisfies a linear recurrence of order at most two. We nontrivially extend the result by excluding the trivial divisor $1$ from consideration, which dramatically increases the analysis complexity. Our first result characterizes all positive integers $N$ such that $S'_N$ satisfies a linear recurrence of order at most two. Moreover, our second result characterizes all positive $N$ such that $L'_N$ satisfies a linear recurrence of order at most two, thus extending considerably a recent result that characterizes $N$ with $L'_N$ being in an arithmetic progression.
