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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

New sums of three cubes


Authors: Andreas-Stephan Elsenhans and Jörg Jahnel
Journal: Math. Comp. 78 (2009), 1227-1230
MSC (2000): Primary 11Y50; Secondary 14G05, 14J28
Published electronically: August 20, 2008
MathSciNet review: 2476583
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Abstract: We report on our search for solutions of the Diophantine equation $ x^3 + y^3 + z^3 = n$ for $ n < 1000$ and  $ \vert x\vert, \vert y\vert, \vert z\vert < 10^{14}$.


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Additional Information

Andreas-Stephan Elsenhans
Affiliation: Mathematisches Institut der Universität Göttingen, Bunsenstrasse 3–5, D-37073 Göttingen, Germany
Email: elsenhan@uni-math.gwdg.de

Jörg Jahnel
Affiliation: Mathematisches Institut der Universität Göttingen, Bunsenstrasse 3–5, D-37073 Göttingen, Germany
Email: jahnel@uni-math.gwdg.de

DOI: http://dx.doi.org/10.1090/S0025-5718-08-02168-6
PII: S 0025-5718(08)02168-6
Keywords: Diophantine equation, sum of three cubes, Elkies' method
Received by editor(s): February 12, 2008
Received by editor(s) in revised form: April 10, 2008
Published electronically: August 20, 2008
Additional Notes: The computer part of this work was executed on the Sun Fire V20z Servers of the Gauss Laboratory for Scientific Computing at the Göttingen Mathematisches Institut. Both authors are grateful to Professor Y. Tschinkel for permission to use these machines as well as to the system administrators for their support.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.