Abstract We prove that a subset A 1, N with align* &₍ ₀1n (N) ^4/5 + o (1) align* contains a subset B such that align* &₍ ₁ 1n = 1. align* 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.
Liu et al. (Sun,) studied this question.
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