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arXiv · 2112.03726

On a density conjecture about unit fractions

Thomas F. Bloom
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Abstract

We prove that any set $A\subset \mathbb{N}$ of positive upper density contains a finite $S\subset A$ such that $\sum_{n\in S}\frac{1}{n}=1$, answering a question of Erdős and Graham.

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Thomas F. Bloom. 2023-10-12. On a density conjecture about unit fractions. https://arxiv.org/abs/2112.03726

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