An extremal problem on the set of noncoprime divisors of a number

P. Erdös, M. Herzog, J. Schönheim

Research output: Contribution to journalArticlepeer-review

Abstract

A combinatorial theorem is established, stating that if a family A1, A2, …, As of subsets of a set M contains every subset of each member, then the complements in M of the A’s have a permutation C1, C2, …, Cs such that Ci ⊃Ai. This is used to determine the minimal size of a maximal set of divisors of a number N no two of them being coprime.

Original languageEnglish
Pages (from-to)408-412
Number of pages5
JournalIsrael Journal of Mathematics
Volume8
Issue number4
DOIs
StatePublished - Dec 1970

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