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Least n such that any n element subset satisfies condition

Source: Chinese Mathematical Olympiad 1998 Problem 3

August 22, 2013
number theory unsolvednumber theory

Problem Statement

Let S={1,2,…,98}S=\{1,2,\ldots ,98\}. Find the least natural number nn such that we can pick out 1010 numbers in any nn-element subset of SS satisfying the following condition: no matter how we equally divide the 1010 numbers into two groups, there exists a number in one group such that it is coprime to the other numbers in that group, meanwhile there also exists a number in the other group such that it is not coprime to any of the other numbers in the same group.
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