On the 8 case of the Sylvester conjecture

Yin, Hongbo

doi:10.1090/tran/8556

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On the 8 case of the Sylvester conjecture

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Yin, Hongbo
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1090/tran/8556
(Publisher version)

https://doi.org/10.48550/arXiv.1912.13338
(Preprint)

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Citation

Yin, H. (2022). On the 8 case of the Sylvester conjecture. Transactions of the American Mathematical Society, 375 (4), 2705-2728. doi:10.1090/tran/8556.

Cite as: https://hdl.handle.net/21.11116/0000-0009-FE82-6

Abstract

Let $p\equiv 8\mod 9$ be a prime. In this paper we give a sufficient
condition such that at least one of $p$ and $p^2$ is the sum of two rational
cubes. This is the first general result on the $8$ case of the so-called
Sylvester conjecture.