An extremal problem on the set of noncoprime divisors of a number (Q2546346)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An extremal problem on the set of noncoprime divisors of a number |
scientific article |
Statements
An extremal problem on the set of noncoprime divisors of a number (English)
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1970
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A combinatorial theorem is established, stating that if a family \(A_1,A_2, \ldots ,A_s\) of subsets of a set \(M\) contains every subset of each member, then the complements in \(M\) of the \(A\)'s have a permutation \(C_1,C_2, \ldots ,C_s\) such that \(C_i \supset A_1\). This is used to determine the minimal size of a maximal set of divisors of a number \(N\) no two of them being coprime.
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