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

 

On sums of seven cubes


Authors: F. Bertault, O. Ramaré and P. Zimmermann
Journal: Math. Comp. 68 (1999), 1303-1310
MSC (1991): Primary 11P05, 11Y50; Secondary 11B13, 11D25, 11D72
Published electronically: February 11, 1999
MathSciNet review: 1642805
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that every integer between 1290741 and $3.375\times 10^{12}$ is a sum of 5 nonnegative cubes, from which we deduce that every integer which is a cubic residue modulo 9 and an invertible cubic residue modulo 37 is a sum of 7 nonnegative cubes.


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Additional Information

F. Bertault
Affiliation: Département de mathématiques, Université de Lille I, 59 655 Villeneuve d’Ascq, France
Email: Francois.Bertault@loria.fr

O. Ramaré
Affiliation: LORIA, BP 101, 54600 Villers-lès-Nancy Cedex, France
Email: ramare@gat.univ-lille1.fr

P. Zimmermann
Email: Paul.Zimmermann@loria.fr

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01071-6
PII: S 0025-5718(99)01071-6
Keywords: Waring's problem for cubes, computational number theory
Received by editor(s): November 4, 1996
Received by editor(s) in revised form: October 28, 1997
Published electronically: February 11, 1999
Article copyright: © Copyright 1999 American Mathematical Society