Arithmetic Progressions Among Powerful Numbers

被引：0
|
作者：
Chan, Tsz Ho [1 ]
机构：
[1] Kennesaw State Univ, Math Dept, Marietta, GA 30060 USA
来源：
JOURNAL OF INTEGER SEQUENCES | 2023年 / 26卷 / 01期
关键词：
powerful number; k-full number; arithmetic progression; abc-conjecture;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study k-term arithmetic progressions N, N + d, ... , N + (k - 1)d of powerful numbers. Unconditionally, we exhibit infinitely many 3-term arithmetic progressions of powerful numbers with d & LE; 5N1/2. Assuming the abc-conjecture, we obtain a nearly tight lower bound on the common difference. We also prove some partial results when k > 4 and pose some open questions.
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页数：10
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