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

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

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?

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redbottle023
redbottle023
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Sets of integers with same sum and same sum of reciprocals

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