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Differences between perfect powers : the Lebesgue-Nagell equation
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Bennett, Michael A. and Siksek, Samir (2023) Differences between perfect powers : the Lebesgue-Nagell equation. Transactions of the American Mathematical Society, 376 (1). pp. 335-370. doi:10.1090/tran/8734 ISSN 0002-9947.
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Official URL: https://doi.org/10.1090/tran/8734
Abstract
We develop a variety of new techniques to treat Diophantine equations of the shape , based upon bounds for linear forms in -adic and complex logarithms, the modularity of Galois representations attached to Frey-Hellegouarch elliptic curves, and machinery from Diophantine approximation. We use these to explicitly determine the set of all coprime integers and , and , with the property that and has no prime divisor exceeding II.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Journal or Publication Title: | Transactions of the American Mathematical Society | ||||||
Publisher: | American Mathematical Society | ||||||
ISSN: | 0002-9947 | ||||||
Official Date: | January 2023 | ||||||
Dates: |
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Volume: | 376 | ||||||
Number: | 1 | ||||||
Page Range: | pp. 335-370 | ||||||
DOI: | 10.1090/tran/8734 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 3 May 2022 | ||||||
Date of first compliant Open Access: | 8 July 2022 | ||||||
Related URLs: | |||||||
Open Access Version: |
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