Let
λ
1
,
…
,
λ
8
{\lambda _1}, \ldots ,{\lambda _8}
be any nonzero real numbers such that not all
λ
j
{\lambda _j}
are of the same sign and not all ratios
λ
j
/
λ
k
{\lambda _j}/{\lambda _k}
are rational. If
η
,
α
\eta ,\alpha
are any real numbers with
0
>
α
>
3
/
70
0 > \alpha > 3/70
then
|
η
+
Σ
j
=
1
8
λ
j
n
j
3
|
>
(
max
n
j
)
−
α
|\eta + \Sigma _{j = 1}^8{\lambda _j}n_j^3| > {(\max {n_j})^{ - \alpha }}
has infinitely many solutions in positive integers
n
j
{n_j}
.