English

Revisiting Unit Fractions That Sum To 1

Number Theory 2016-03-24 v1

Abstract

This paper is a continuation of a previous paper. Here, as there, we examine the problem of finding the maximum number of terms in a partial sequence of distinct unit fractions larger than 1/100 that sums to 1. In the previous paper, we found that the maximum number of terms is 42 and introduced a method for showing that. In this paper, we demonstrate that there are 27 possible solutions with 42 terms, and discuss how primes show that no 43-term solution exists.

Keywords

Cite

@article{arxiv.1603.07035,
  title  = {Revisiting Unit Fractions That Sum To 1},
  author = {Yutaka Nishiyama},
  journal= {arXiv preprint arXiv:1603.07035},
  year   = {2016}
}

Comments

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R2 v1 2026-06-22T13:16:41.468Z