## An improved estimate for certain Diophantine inequalities

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- by Ming Chit Liu, Shu Ming Ng and Kai Man Tsang
- Proc. Amer. Math. Soc.
**78**(1980), 457-463 - DOI: https://doi.org/10.1090/S0002-9939-1980-0556611-3
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## Abstract:

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

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## Bibliographic Information

- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**78**(1980), 457-463 - MSC: Primary 10B45; Secondary 10F05
- DOI: https://doi.org/10.1090/S0002-9939-1980-0556611-3
- MathSciNet review: 556611