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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 217.30701

**Autor: ** Erdös, Paul; Herzog, M.; Schönheim, J.

**Title: ** An extremal problem on the set of noncoprime divisors of a number (In English)

**Source: ** Isr. J. Math. 8, 408-412 (1970).

**Review: ** 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} \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.

**Classif.: ** * 05A05 Combinatorial choice problems

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