Problem Statement
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\[1=\frac{1}{n_1}+\cdots+\frac{1}{n_k}?\]
Categories:
Number Theory Unit Fractions
Progress
The answer is yes, proved by Croot [Cr01].Source: erdosproblems.com/286 | Last verified: January 14, 2026