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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Bounds for integral solutions of diagonal cubic equations
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by Ka Hin Leung PDF
Trans. Amer. Math. Soc. 278 (1983), 183-195 Request permission

Abstract:

It was proved by Davenport [3] that for the nonzero integral ${\lambda _i}$ the equation ${\lambda _1}x_1^3 + \cdots + {\lambda _8}x_8^3 = 0$ always has a nontrivial integral solution. In this paper, we investigate the bounds of nontrivial integral solutions in terms of ${\lambda _1}, \ldots ,{\lambda _8}$.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 278 (1983), 183-195
  • MSC: Primary 11D25; Secondary 11P55
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0697069-0
  • MathSciNet review: 697069