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

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 ( n 2 ). Their proof depended upon a two parameter solution of (1) due to Richmond and is very complicated.