OPEN
This is open, and cannot be resolved with a finite computation.
Let $a/b\in \mathbb{Q}_{>0}$ with $b$ squarefree. Are there integers $1<n_1<\cdots<n_k$, each the product of two distinct primes, such that\[\frac{a}{b}=\frac{1}{n_1}+\cdots+\frac{1}{n_k}?\]
For $n_i$ the product of three distinct primes, this is true when $b=1$, as proved by Butler, Erdős and Graham
[BEG15] (this paper is perhaps Erdős' last paper, appearing 19 years after his death).
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When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:
T. F. Bloom, Erdős Problem #306, https://www.erdosproblems.com/306, accessed 2026-01-16
