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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