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An effective seven cube theorem

Published online by Cambridge University Press:  17 April 2009

R. J. Cook
R. J. Cook
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S37RH, England.
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Abstract

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It is well-known that every sufficiently large positive integer is the sum of seven cubes. Both proofs of this result, due to Linnik and Watson, are ineffective. Here we show that Watson's proof may be made effective.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 30 , Issue 3 , December 1984 , pp. 381 - 385
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Davenport, H., Multiplicative number theory, 2nd edition (Springer-Verlag, Berlin, Heidelberg, New York, 1980).CrossRefGoogle Scholar
[2]Hooley, C., “On Waring's problem for seven cubes” (University of London Number Theory Seminar, 1984).Google Scholar
[3]Linnik, Ju. V., “On the representation of large numbers as sums of seven cubes”, Mat. Sb. 12 (1943), 218–224.Google Scholar
[4]Watson, G.L., “A proof of the seven cube theorem”, J. London Math. Soc. 26 (1951), 153–156.CrossRefGoogle Scholar