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arXiv · 2109.12217

Egyptian Fractions with Denominators from Sequences Closed Under Doubling

David Eppstein
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Abstract

Resolving a conjecture of Zhi-Wei Sun, we prove that every rational number can be represented as a sum of distinct unit fractions whose denominators are practical numbers. The same method applies to allowed denominators that are closed under multiplication by two and include a multiple of every positive integer, including the odious numbers, evil numbers, Hardy-Ramanujan numbers, Jordan-Polya numbers, and fibbinary numbers.

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David Eppstein. 2021-09-24. Egyptian Fractions with Denominators from Sequences Closed Under Doubling. https://arxiv.org/abs/2109.12217

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