English

Egyptian Fractions with Denominators from Sequences Closed Under Doubling

Number Theory 2021-09-28 v1

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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Cite

@article{arxiv.2109.12217,
  title  = {Egyptian Fractions with Denominators from Sequences Closed Under Doubling},
  author = {David Eppstein},
  journal= {arXiv preprint arXiv:2109.12217},
  year   = {2021}
}

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6 pages