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paper

86 unknowns for Hilbert's tenth problem over the rationals

arXiv ↗
ID
2610.20691
分类
—
首次捕获
2026-10-16
状态
unread
作者
Zhi-Wei Sun
信号
SI 49

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  • 2026-10-16Scholar Inbox · 相关分 49
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摘要

Recently, Hilbert's Tenth Problem over the field $\mathbb Q$ of rational numbers was solved negatively by OpenAI based on a five-contact height estimate and a pole-parity construction. In this paper, we prove further that there is no algorithm to decide for any polynomial $f(x_1,\ldots,x_{86})$ with integer coefficients whether the equation $f(x_1,\ldots,x_{86})=0$ has solutions with $x_1,\ldots,x_{86}\in\mathbb Q$.

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