Consider the set . 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.
Just take the set T = {0, 1, 2, 3, ..., 2^k}.
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. 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.
