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On sums of seven cubes
Author(s):
F.
Bertault;
O.
Ramaré;
P.
Zimmermann.
Journal:
Math. Comp.
68
(1999),
1303-1310.
MSC (1991):
Primary 11P05, 11Y50;
Secondary 11B13, 11D25, 11D72
Posted:
February 11, 1999
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Abstract:
We show that every integer between 1290741 and  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.
References:
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- 2.
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- 3.
- J.M. Deshouillers, F. Hennecart and B. Landreau, private communication.
- 4.
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- 5.
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 '', Math. Zeitschrift (1922) Vol 12, pp 161-188. - 7.
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- 8.
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- 10.
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- 15.
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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:
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
Posted:
February 11, 1999
Copyright of article:
Copyright
1999,
American Mathematical Society
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