# Integers that are sums of two rational fifth powers

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- 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

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