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Title: On the Lebesgue-Nagell equation and related subjects
Author: Barros, Carlos Filipe
ISNI:       0000 0004 2705 958X
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2010
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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:  DOI: Not available
Keywords: QA Mathematics