### Abstract

A combinatorial theorem is established, stating that if a family A_{1}, A_{2}, …, 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}, …, C_{s} such that C_{i} ⊃A_{i}. 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 language | English |
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Pages (from-to) | 408-412 |

Number of pages | 5 |

Journal | Israel Journal of Mathematics |

Volume | 8 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 1970 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Erdös, P., Herzog, M., & Schönheim, J. (1970). An extremal problem on the set of noncoprime divisors of a number.

*Israel Journal of Mathematics*,*8*(4), 408-412. https://doi.org/10.1007/BF02798688