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On the representation of positive integers as sums of three cubes of positive rational numbers

Published online by Cambridge University Press:  26 February 2010

L. J. Mordell
L. J. Mordell
Affiliation:
St. John's College, Cambridge.
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Extract

A one parameter solution of th equation

was given by Ryley in 1825. Others were found by Richmond and myself. In the Landau memorial volume [1] recently published, there appears a joint paper, with the above title, of Davenport and Landau dating from 1935. They prove that if n is a positive integer, then positive rational solutions of (1) exist with denominators of order of magnitude O(n2). Their proof depended upon a two parameter solution of (1) due to Richmond and is very complicated.

Type
Research Article
Information
Mathematika , Volume 18 , Issue 1 , June 1971 , pp. 98 - 99
Copyright
Copyright © University College London 1971

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References

1.Abhandlungen aus Zahlentheorie und Analysis zur Erinnerung an Edmund Landau (1877-1938) Veb Deutscher Verlag der Wissenschaften (Berlin 1969) 51–53.Google Scholar
2.On Ryley's solution of x3+y3+z3 = n, J. London Math. Soc. 7 (1942) 194–196.Google Scholar