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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An improved estimate for certain Diophantine inequalities
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by Ming Chit Liu, Shu Ming Ng and Kai Man Tsang PDF
Proc. Amer. Math. Soc. 78 (1980), 457-463 Request permission

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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Additional 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