Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-29T20:56:29.788Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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