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Find the smallest integer k which satisfy the condition

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September 20, 2010
pigeonhole principlenumber theoryDivisibilityIMO Shortlist

Problem Statement

Let SS be the set of all the odd positive integers that are not multiples of 55 and that are less than 30m30m, mm being an arbitrary positive integer. What is the smallest integer kk such that in any subset of kk integers from SS there must be two different integers, one of which divides the other?
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