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Least n such that any n-subset of A contains x,y with x|y

Source: Romanian TST 1997

September 17, 2011
floor functionceiling functionnumber theoryprime numberscombinatorics proposedcombinatoricsposet

Problem Statement

Let p,q,rp,q,r be distinct prime numbers and let A={paqbrc∣0≤a,b,c≤5}A=\{p^aq^br^c\mid 0\le a,b,c\le 5\} Find the least n∈Nn\in\mathbb{N} such that for any B⊂AB\subset A where ∣B∣=n|B|=n, has elements xx and yy such that xx divides yy.
Ioan Tomescu
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