Let $A$, $B$ be two distinct sets of natural numbers. Is it possible to have $\ \sum_{a\in A}a\,=\,\sum_{b\in B}b\ $ and $\ \sum_{a\in A}1/a\,=\,\sum_{b\in B}1/b\ $ at the same time?
Sets of integers with same sum and same sum of reciprocals
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