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arXiv · 2310.20021

Sextic polynomials in two variables do not represent all non-negative integers

Stanley Yao Xiao
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Abstract

In this paper we prove that for all degree $6$ polynomials with rational coefficients that $F(\mathbb{Z}^2) \neq \mathbb{Z}_{\geq 0}$. The answers a question of B. Poonen and J. S. Lew in the degree 6 case. This work builds on previous work with S. Yamagishi.

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Stanley Yao Xiao. 2023-10-30. Sextic polynomials in two variables do not represent all non-negative integers. https://arxiv.org/abs/2310.20021

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