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

2023/07/11 by Xiao, Stanley Yao, Yamagishi, Shuntaro
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2307.05712

Abstract

In this paper, we prove that there does not exist F ∈ ℚ[x,y] of degree 4 such that F(ℤ²) = ℤ_{≥ 0}. In particular, this answers a question by John S. Lew and Bjorn Poonen for quartic polynomials.

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