论文标题
当自然数量的非平凡,小的划分处于算术中
When the Nontrivial, Small Divisors of a Natural Number are in Arithmetic Progression
论文作者
论文摘要
Iannucci考虑了不超过$ \ sqrt {n} $的天然数字$ n $的正分离,并找到了所有形式的数字,这些数字在算术中都处于算术状态。在本文中,我们通过排除琐碎的除数$ 1 $和$ \ sqrt {n} $(当$ n $是平方)来概括了Iannucci的结果。令人惊讶的是,我们的算术进度的长度不能超过$ 5 $。
Iannucci considered the positive divisors of a natural number $n$ that do not exceed $\sqrt{n}$ and found all forms of numbers whose such divisors are in arithmetic progression. In this paper, we generalize Iannucci's result by excluding the trivial divisors $1$ and $\sqrt{n}$ (when $n$ is a square). Surprisingly, the length of our arithmetic progression cannot exceed $5$.