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- Jun 20, 2014

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Given a nonempty set $A$ of positive integers, let $B$ be a subset of $A$ such that $\dfrac{m}{2}\notin A$ whenever $m\in B$. If $n$ is a positive number, prove that the partitions of $n$ into distinct parts selected from $A$ is equinumerous with the partitions of $n$ into parts selected from $B$.

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