Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
420143 | Discrete Applied Mathematics | 2012 | 6 Pages |
Abstract
Let p1,p2,…,pnp1,p2,…,pn be distinct primes. In 1970, Erdős, Herzog and Schönheim proved that if DD, |D|=m|D|=m, is a set of divisors of N=p1α1⋯pnαn, α1≥α2≥⋯≥αnα1≥α2≥⋯≥αn, no two members of the set being coprime and if no additional member may be included in DD without contradicting this requirement then m≥αn∏i=1n−1(αi+1). They asked to determine all sets DD such that the equality holds. In this paper we solve this problem. We also pose several open problems for further research.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Yong-Gao Chen, Cui-Ying Hu,