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New sums of three cubes

Author(s): Andreas-Stephan Elsenhans; Jörg Jahnel.
Journal: Math. Comp.
MSC (2000): Primary 11Y50; Secondary 14G05, 14J28
Posted: August 20, 2008
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Abstract | References | Similar articles | Additional information

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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Beck, M., Pine, E., Tarrant, W., and Yarbrough Jensen, K.: New integer representations as the sum of three cubes, Math. Comp. 76 (2007), 1683-1690. MR 2299795 (2007m:11170)

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Elsenhans, A.-S. and Jahnel, J.: List of solutions of $ x^3 + y^3 + z^3 = n$ for  $ n < 1\,000$ neither a cube nor twice a cube, available at: http://www.uni-math.gwdg.de/jahnel/ threecubes_20070419.txt.

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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: 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
Posted: 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.
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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