Prove that if 100 integers are chosen from 1,2,...,200, and one of the integers chosen is less than 16, then there are two chosen numbers such that one of them is divisible by the other. Thanks in advance!
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1The problem is solved at http://ohkawa.cc.it-hiroshima.ac.jp/AoPS.pdf/MathStudio/Q4%20coprime%20numbers%20_%20200.pdf where it seems to involve a certain amount of looking at cases. – Gerry Myerson Jul 13 '14 at 01:42