Abstract/Details

Ahmes expansions over certain Euclidean domains


2009 2009

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Abstract (summary)

It is well-known that if a and b are nonzero natural numbers then there exist nonzero natural numbers p0, p1,···, pn such that [special characters omitted], where p0 < p 1 < … < pn. Such expansions of [special characters omitted] are called "Ahmes expansions" of [special characters omitted]. This thesis is dedicated to extending this notion to the context of an arbitrary Euclidean domain. After a brief history and essential background on Ahmes expansions of positive rational numbers, the author advances an algorithm that can be utilized to produce Ahmes-type expansions of proper fractions over the integers and polynomial rings over a field, respectively. The author then develops several results related to the analogous concept of "length" of proper fractions for these specific Euclidean domains.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Ahmes expansions; Egyptian expansions; Unit fraction expansion
Title
Ahmes expansions over certain Euclidean domains
Author
Houston, Matthew
Number of pages
37
Publication year
2009
Degree date
2009
School code
0390
Source
MAI 47/05M, Masters Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9781109141986
Advisor
Hetzel, Andrew J.
Committee member
Ablamowicz, Rafal; Mills, Allan
University/institution
Tennessee Technological University
Department
Mathematics
University location
United States -- Tennessee
Degree
M.S.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
1464339
ProQuest document ID
305066710
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/305066710/fulltextPDF
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