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Classical and modular approaches to exponential Diophantine equations - II. The Lebesgue-Nagell equation
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UNSPECIFIED (2006) Classical and modular approaches to exponential Diophantine equations - II. The Lebesgue-Nagell equation. COMPOSITIO MATHEMATICA, 142 (1). pp. 31-62. doi:10.1112/S0010437X05001739 ISSN 0010-437X.
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Official URL: http://dx.doi.org/10.1112/S0010437X05001739
Abstract
This is the second in a series of papers where we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat's Last Theorem. In this paper we use a general and powerful new lower bound for linear forms in three logarithms, together with a combination of classical, elementary and substantially improved modular methods to solve completely the Lebesgue-Nagell equation x(2) + D = y(n), x, y integers, n >= 3, for D in the range 1 <= D <= 100.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | COMPOSITIO MATHEMATICA | ||||
Publisher: | LONDON MATH SOC | ||||
ISSN: | 0010-437X | ||||
Official Date: | January 2006 | ||||
Dates: |
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Volume: | 142 | ||||
Number: | 1 | ||||
Number of Pages: | 32 | ||||
Page Range: | pp. 31-62 | ||||
DOI: | 10.1112/S0010437X05001739 | ||||
Publication Status: | Published |
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