On a problem of Erdős on integers, none of which divides the product of k others

Authors:
Tsz Ho Chan;Ervin Gyri;András Sárközy
Affiliations:
Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA;Rényi Institute, P.O.B. 127, Budapest, H-1364, Hungary;Eötvös Loránd University, Department of Algebra and Number Theory, Budapest, Pázmány Péter sétány 1/C, H-1117, Hungary
Venue:
European Journal of Combinatorics
Year:
2010

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On sets of integers, none of which divides the product of k others

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Abstract

Erdos estimated the maximal number of integers selected from {1,2,...,N}, so that none of them divides the product of two others. In this paper, Erdos' problem is extended to sets of integers such that none of them divides the product of k others. The proofs use combinatorial results.