Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.535338
Title: On the Lebesgue-Nagell equation and related subjects
Author: Barros, Carlos Filipe
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2010
Availability of Full Text:
Access from EThOS:
Access from Institution:
Abstract:
The work of Cohn [Coh93] and Bugeaud, Mignotte and Siksek [BMS06] solves the Lebesgue-Naguel equation x2 + D = yn, x, y integers, n ≥ 3 for D a integer in the range 1 ≤ D ≤ 100. We propose to do the same for D in the range -100 ≤ D ≤ -1. For that we will use techniques that go from the most classical ones, ideal factorization over number fields and Thue equations, to the most modern approach to Diophantine equations, Frey curves and the Modular approach, passing by linear forms in logarithms.
Supervisor: Not available Sponsor: Fundação para a Ciência e a Tecnologia (FCT) (SFRH/BD/29433/2006)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.535338  DOI: Not available
Keywords: QA Mathematics
Share: