Arithmetic Progressions Among Powerful Numbers
Department
Mathematics
Document Type
Article
Publication Date
1-1-2023
Abstract
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 ≤ 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.
Journal Title
Journal of Integer Sequences
Volume
23
Issue
1
Digital Object Identifier (DOI)
NA
COinS