On exactly \(m\) times covers
type: Item
instance of: scholarly article
title: On exactly \(m\) times covers
zbMATH Open document ID: 0768.11001
DOI: 10.1007/BF02773696
published in: Israel Journal of Mathematics
publication date: 1993-06-29T00:00:00Z
review text: Let \(a+n\mathbb{Z}\) denote the arithmetic sequence \(\{x\in \mathbb{Z}: x\equiv a\pmod n\}\). In this paper, the author proves that if every integer is covered by \(a_ i = n_ i\mathbb{Z}\) \((i = 1,2,\dots,k)\) exactly \(m\) times, then for each \(n = 1,\dots,m\), there exist at least \(m\choose n\) subsets \(I\) of \(\{1,\dots,k\}\) such that \(\sum_{i \in I}1/n_ i\) equals \(n\). The bound \(m\choose n\) is best possible.
Mathematics Subject Classification ID: 11A07
zbMATH DE Number: 219362
zbMATH Keywords: arithmetic sequence
zbMATH Keywords: exact covering
author: Zhi-Wei Sun
MaRDI profile type: Publication
cites work: Some Trigonometric Identities Related to Exact Covers
cites work: Unsolved problems in number theory
cites work: On m times covering systems of congruences
cites work: Q3481761
cites work: Q4010185
cites work: Q3475310
full work available at URL: https://doi.org/10.1007/bf02773696
OpenAlex ID: W1972907485
reviewed by: Ke Zhao
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description: scientific article; zbMATH DE number 219362