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Let $k\geq 2$. Is it true that there exists an interval $I$ of width $(e-1+o(1))k$ and integers $n_1<\cdots<n_k\in I$ such that \[1=\frac{1}{n_1}+\cdots+\frac{1}{n_k}?\]
#286
:
[ErGr80]
number theory
,
unit fractions
The answer is yes, proved by Croot
[Cr01]
.
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