论文信息 - On a problem of Erdos on integers, none of which divides the product of k others

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

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.

András Sárközy | Ervin Györi | Tsz Ho Chan

[1] Richard H. Schelp,et al. An extremal problem for paths in bipartite graphs , 1984, J. Graph Theory.

[2] Paul Erdös,et al. On product representations of powers, I , 1995, Eur. J. Comb..

[3] H. Hanani. The Existence and Construction of Balanced Incomplete Block Designs , 1961 .

[4] Prince Camille de Polignac. On a Problem in Combinations , 1866 .

[5] Ervin Györi. C6-free bipartite graphs and product representation of squares , 1997, Discret. Math..

[6] P. Erdös,et al. Families of finite sets in which no set is covered by the union ofr others , 1985 .

[7] R. Ahlswede,et al. On the density of primitive sets , 2004 .