Abstract
It is proved that if
C
(x
1
...,
x
n) is any cubic form in
n
variables, with integral coefficients, then the equation
C
(
x
1
x
n
) = 0 has a solution in integers
x
1
...,
x
n not all 0, provided n is at least 29. This is an improvement on a previous result (Davenport 1959).
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4. Vinogradov I. M. 1954 The method of trigonometrical sum s the theory of numbers. T ra n slated revised and an n o tated by K . F . R o th an d A. D avenport. L ondon: Interscience Publishers.
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