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 16. This is an improvement upon earlier results (Davenport 1959, 1962).
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