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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 ISSN 0021-8693.
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Official URL: http://dx.doi.org/10.1016/j.jalgebra.2009.03.010
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, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Journal of Algebra | ||||
| Publisher: | Academic Press Inc Elsevier Science | ||||
| ISSN: | 0021-8693 | ||||
| Official Date: | 1 August 2009 | ||||
| Dates: |
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| 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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