Home WakeSpace Scholarship › Electronic Theses and Dissertations

Integers that are sums of two rational fifth powers

Electronic Theses and Dissertations

Item Files

Item Details

title
Integers that are sums of two rational fifth powers
author
Varlack, Japheth Abiah
abstract
We are interested in answering the question: What is the smallest positive integer K such that the equation x^5 + y^5 = K has no integer solutions but does have rational solutions? To this end, suppose K is a positive integer such that the equation x^5 + y^5 = K has no integer solutions. We describe one strategy for computing all of the rational solutions to the equation x^5 + y^5 = K, and we describe one strategy for verifying that no rational solutions exist. In the case where both of these strategies fail, we describe potential ways to extend this work.
subject
computational
frey curves
hyperelliptic curves
magma
number theory
rational solutions
contributor
Rouse, Jeremy (advisor)
Rouse, Jeremy (committee member)
Parsley, Jason (committee member)
Bourdon, Abbey (committee member)
date
2024-05-23T08:36:15Z (accessioned)
2024-05-23T08:36:15Z (available)
2024 (issued)
degree
Mathematics (discipline)
identifier
http://hdl.handle.net/10339/109427 (uri)
language
en (iso)
publisher
Wake Forest University
type
Thesis

Usage Statistics