Problem

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Tags: number theory



For integer $a$, $a \neq 0$, $v_2(a)$ is greatest nonnegative integer $k$ such that $2^k | a$. For given $n \in \mathbb{N}$ determine highest possible cardinality of subset $A$ of set $ \{1,2,3,...,2^n \} $ with following property: For all $x, y \in A$, $x \neq y$, number $v_2(x-y)$ is even.