On the Lebesgue-Nagell equation and related subjects
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 classica...
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University of Warwick
2010
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ndltd-bl.uk-oai-ethos.bl.uk-5353382015-03-20T03:41:11ZOn the Lebesgue-Nagell equation and related subjectsBarros, Carlos Filipe2010The 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.510QA MathematicsUniversity of Warwickhttp://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.535338http://wrap.warwick.ac.uk/35160/Electronic Thesis or Dissertation |
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NDLTD |
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NDLTD |
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510 QA Mathematics |
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510 QA Mathematics Barros, Carlos Filipe On the Lebesgue-Nagell equation and related subjects |
| description |
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. |
| author |
Barros, Carlos Filipe |
| author_facet |
Barros, Carlos Filipe |
| author_sort |
Barros, Carlos Filipe |
| title |
On the Lebesgue-Nagell equation and related subjects |
| title_short |
On the Lebesgue-Nagell equation and related subjects |
| title_full |
On the Lebesgue-Nagell equation and related subjects |
| title_fullStr |
On the Lebesgue-Nagell equation and related subjects |
| title_full_unstemmed |
On the Lebesgue-Nagell equation and related subjects |
| title_sort |
on the lebesgue-nagell equation and related subjects |
| publisher |
University of Warwick |
| publishDate |
2010 |
| url |
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.535338 |
| work_keys_str_mv |
AT barroscarlosfilipe onthelebesguenagellequationandrelatedsubjects |
| _version_ |
1716782541701120000 |