On the Number of Representations of One as the Sum of Unit Fractions

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dc.contributor.authorCrawford, Matthew Brendanen
dc.contributor.committeechairPalsson, Eyvindur Arien
dc.contributor.committeememberMendelson, Samuelen
dc.contributor.committeememberOrr, Daniel D.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2019-06-25T08:00:37Zen
dc.date.available2019-06-25T08:00:37Zen
dc.date.issued2019-06-24en
dc.description.abstractThe 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.en
dc.description.abstractgeneralExpressing 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.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:20999en
dc.identifier.urihttp://hdl.handle.net/10919/90573en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectEgyptian Fractionen
dc.subjectUnit Fractionen
dc.subjectCombinatoricsen
dc.subjectNumber Theoryen
dc.titleOn the Number of Representations of One as the Sum of Unit Fractionsen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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