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Does every set $A\subseteq \mathbb{N}$ of positive density contain some finite $S\subset A$ such that $\sum_{n\in S}\frac{1}{n}=1$?
#298
:
[ErGr80]
[Er92c]
number theory
,
unit fractions
The answer is yes, proved by Bloom
[Bl21]
.
See also
[46]
and
[47]
.
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