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Perfect powers that are sums of consecutive cubes
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Bennett, Michael A., Patel, Vandita and Siksek, Samir (2017) Perfect powers that are sums of consecutive cubes. Mathematika, 63 (1). pp. 230-249. doi:10.1112/S0025579316000231 ISSN 0025-5793.
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Official URL: http://dx.doi.org/10.1112/S0025579316000231
Abstract
Euler noted the relation 63 = 33 + 43 + 53 and asked for other
instances of cubes that are sums of consecutive cubes. Similar problems have been studied by Cunningham, Catalan, Gennochi, Lucas, Pagliani, Cassels, Uchiyama, Stroeker and Zhongfeng Zhang. In particular Stroeker determined all squares that can be written as a sum of at most 50 consecutive cubes. We generalize Stroeker’s work by determining all perfect powers that are sums of at most 50 consecutive cubes. Our methods include descent, linear forms in two logarithms, and Frey-Hellegouarch curves.
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): | Cube, Exponents (Algebra), Logarithms | ||||||||
Journal or Publication Title: | Mathematika | ||||||||
Publisher: | London Mathematical Society | ||||||||
ISSN: | 0025-5793 | ||||||||
Official Date: | January 2017 | ||||||||
Dates: |
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Volume: | 63 | ||||||||
Number: | 1 | ||||||||
Page Range: | pp. 230-249 | ||||||||
DOI: | 10.1112/S0025579316000231 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 25 August 2016 | ||||||||
Date of first compliant Open Access: | 1 November 2016 | ||||||||
Funder: | Natural Sciences and Engineering Research Council of Canada (NSERC), Engineering and Physical Sciences Research Council (EPSRC) | ||||||||
Grant number: | EP/K034383/1 (EPSRC) |
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