### 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 - 1970 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Israel Journal of Mathematics*,

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

**An extremal problem on the set of noncoprime divisors of a number.** / Erdős, P.; Herzog, M.; Schönheim, J.

Research output: Contribution to journal › Article

*Israel Journal of Mathematics*, vol. 8, no. 4, pp. 408-412. https://doi.org/10.1007/BF02798688

}

TY - JOUR

T1 - An extremal problem on the set of noncoprime divisors of a number

AU - Erdős, P.

AU - Herzog, M.

AU - Schönheim, J.

PY - 1970

Y1 - 1970

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=1842752541&partnerID=8YFLogxK

U2 - 10.1007/BF02798688

DO - 10.1007/BF02798688

M3 - Article

VL - 8

SP - 408

EP - 412

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 4

ER -