Bounds for integral solutions of diagonal cubic equations

Leung, Ka Hin

doi:10.1090/S0002-9947-1983-0697069-0

Bounds for integral solutions of diagonal cubic equations
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by Ka Hin Leung

Trans. Amer. Math. Soc. 278 (1983), 183-195

DOI: https://doi.org/10.1090/S0002-9947-1983-0697069-0

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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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