On the $8$ case of Sylvester Conjecture

Hongbo Yin

On the $8$ case of Sylvester Conjecture

Number Theory 2021-09-17 v2

Authors: Hongbo Yin

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.

Keywords

sylvester conjecture rational cubes prime numbers sum of two cubes modular arithmetic

Cite

@article{arxiv.1912.13338,
  title  = {On the $8$ case of Sylvester Conjecture},
  author = {Hongbo Yin},
  journal= {arXiv preprint arXiv:1912.13338},
  year   = {2021}
}

Comments

This is an improved version of the previous work. I get a much simpler but stronger result in this new version. Based on the suggestions of referee, I add or rewrite some of the proofs in order to make it easier to read. I also modify the computation mistakes and typos. This version is accepted to appear in Tran.AMS

On the $8$ case of Sylvester Conjecture

Abstract

Keywords

Cite

Comments

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