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Perfect powers expressible as sums of two cubes

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Chen, Imin and Siksek, Samir (2009) Perfect powers expressible as sums of two cubes. Journal of Algebra, Vol.322 (No.3 Sp. Iss. SI). pp. 638-656. doi:10.1016/j.jalgebra.2009.03.010

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Official URL: http://dx.doi.org/10.1016/j.jalgebra.2009.03.010

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Abstract

Let >= 3. This paper is concerned with the equation a(3) + b(3) = c(n). which we attack using a combination of the modular approach (via Frey curves and Galois representations) with obstructions to the solutions that are of Brauer-Manin type. We shall show that there are no solutions in coprime, non-zero integers a, b, c, for a set of prime exponents n having Dirichlet density 28219/0.628 approximate to and for a set of exponents n having natural density 1. (C) 2009 Elsevier Inc. All rights reserved.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Journal or Publication Title: Journal of Algebra
Publisher: Academic Press Inc Elsevier Science
ISSN: 0021-8693
Official Date: 1 August 2009
Dates:
DateEvent
1 August 2009Published
Volume: Vol.322
Number: No.3 Sp. Iss. SI
Number of Pages: 19
Page Range: pp. 638-656
DOI: 10.1016/j.jalgebra.2009.03.010
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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