The Egyptian Fractions of One problem (EFO), asks the following question: Given a positive integer n, how many ways can 1 be expressed as the sum of n non-increasing unit fractions? In this paper, we verify a result concerning the EFO problem for n=8, and show the computational complexity of the problem can be severely lessened by new theorems concerning the structure of solutions to the EFO problem. / Master of Science / Expressing numbers as fractions has been the subject of one’s education since antiquity. This paper shows how we can write the number 1 as the sum of uniquely behaved fractions called “unit fractions”, that is, fractions with 1 in the numerator and some natural counting number in the denominator. Counting the number of ways this can be done reveals certain properties about the prime numbers, and how they interact with each other, as well as pushes the boundaries of computing power.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/90573 |
| Date | 24 June 2019 |
| Creators | Crawford, Matthew Brendan |
| Contributors | Mathematics, Palsson, Eyvindur Ari, Mendelson, Samuel, Orr, Daniel D. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
Page generated in 0.0019 seconds