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Consider the set \(S = \{0, 1, 2, \ldots, 3^k-1\}\). Prove that one can choose T to be a \(2^k\) element subset of S such that none of the elements of T can be represented as the arithmetic mean of two distinct elements of T. 

 Jul 3, 2020
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You should try using induction.

 Jul 3, 2020

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