Revisiting Unit Fractions That Sum To 1
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 43term solution exists.
 Publication:

arXiv eprints
 Pub Date:
 March 2016
 arXiv:
 arXiv:1603.07035
 Bibcode:
 2016arXiv160307035N
 Keywords:

 Mathematics  Number Theory
 EPrint:
 1 Figure