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Virginia Polytechnic Institute and State University
The Fermat equation over quadratic fields
Abstract
dc:description.abstractIn this thesis we attempt to generalize some of Kummer's work on Fermat's Last Theorem over the rational numbers to quadratic fields. In particular, under certain congruence conditions it is shown that the Fermat equation of exponent p has no solution over Q(√m) when p is a m-regular prime. Completely analogous to the work of Kummer, it is shown that m-regular primes can be described in terms of the generalized Bernoulli numbers. When p = 3,5 and 7, an explicit, easily computable criterion is given for m-regularity.
Degree
thesis:*- Name thesis:degree_name
- Ph. D.
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Polytechnic Institute and State University
- Year dc:date.issued
- 1982
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Hao, Hsin-Seng Fred
- Chair dc:contributor.committeechair
-
- Parry, Charles J.
- Committee members dc:contributor.committeemember
-
- Aull, Charles E.
- Brown, E.A.
- Green, E.L.
- Prather, Carl
Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
- Language dc:language.iso
- en_US
Identifiers
dc:identifier.*- Handle dc:identifier.uri
- http://hdl.handle.net/10919/81015
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/81015