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Proceedings of the American Mathematical Society

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An improved estimate for certain Diophantine inequalities


Authors: Ming Chit Liu, Shu Ming Ng and Kai Man Tsang
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
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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 ${n_j}$.


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Article copyright: © Copyright 1980 American Mathematical Society