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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 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
Proc. Amer. Math. Soc. 78 (1980), 457-463
DOI: https://doi.org/10.1090/S0002-9939-1980-0556611-3

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