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A multi-frey approach to some multi-parameter families of diophantine equations
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Bugeaud, Yann, Mignotte, Maurice and Siksek, Samir (2008) A multi-frey approach to some multi-parameter families of diophantine equations. Canadian Journal of Mathematics, Vol.60 (No.3). pp. 491-519. doi:DOI:10.4153/CJM-2008-024-9 ISSN 0008-414X.
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Official URL: http://dx.doi.org/10.4153/CJM-2008-024-9
Abstract
We solve several multi-parameter families of binomial Thue equations of arbitrary degree; for example, we solve the equation
5(u)x(n) - 2(r)3(s)y(n) = +/- 1,
in non-zero integers x, y and positive integers u, r, s and n >= 3. Our approach uses several Frey curves simultaneously, Galois representations and level-lowering, new lower bounds for linear forms in 3 logarithms due to Mignotte and a famous theorem of Bennett on binomial Thue equations.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Curves, Elliptic, Diophantine equations, Logarithms | ||||
Journal or Publication Title: | Canadian Journal of Mathematics | ||||
Publisher: | University of Toronto Press | ||||
ISSN: | 0008-414X | ||||
Official Date: | June 2008 | ||||
Dates: |
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Volume: | Vol.60 | ||||
Number: | No.3 | ||||
Number of Pages: | 29 | ||||
Page Range: | pp. 491-519 | ||||
DOI: | DOI:10.4153/CJM-2008-024-9 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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