On further questions regarding unit fractions

arxiv（2024）

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Abstract

We prove that a subset A⊆ [1, N] with ∑_n∈ A1/n≥ (log N)^4/5 + o(1) contains a subset B such that ∑_n∈ B1/n = 1. Our techniques refine those of Croot and of Bloom. Using our refinements, we additionally consider a number of questions regarding unit fractions due to Erdős and Graham.

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