论文标题
强大数字之间的算术进程
Arithmetic progressions among powerful numbers
论文作者
论文摘要
在本文中，我们研究了$ k $ - term算术进度$ n，n+d，...，n+（k-1）d $ a os of stuct of stuct of stuctiment。在$ abc $ - 注射器下，我们获得$ d \gg_εn^{1/2-ε} $。另一方面，有很多$ 3 $ term的算术算术进程是有力数字的，$ d \ ll n^{1/2} $无条件地。当$ k \ ge 4 $并提出一些开放问题时，我们还证明了一些部分结果。
In this paper, we study $k$-term arithmetic progressions $N, N+d, ..., N+(k-1)d$ of powerful numbers. Under the $abc$-conjecture, we obtain $d \gg_εN^{1/2 - ε}$. On the other hand, there exist infinitely many $3$-term arithmetic progressions of powerful numbers with $d \ll N^{1/2}$ unconditionally. We also prove some partial results when $k \ge 4$ and pose some open questions.
