PreprintarXiv licencearXiv
86 unknowns for Hilbert's tenth problem over the rationals
Abstract
Recently, Hilbert's Tenth Problem over the field 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 P(x1,…,x86) with integer coefficients whether the equation P(x1,…,x86)=0 has solutions with x1,…,x86∈ℚ.
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BibTeX
@misc{sun2026unknowns,
title = {{86 unknowns for Hilbert's tenth problem over the rationals}},
author = {Zhi-Wei Sun},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20691},
eprint = {2610.20691},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20691},
}
RIS
TY - UNPB
TI - 86 unknowns for Hilbert's tenth problem over the rationals
AU - Zhi-Wei Sun
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.20691
UR - https://arxiv.org/abs/2610.20691
AB - Recently, Hilbert's Tenth Problem over the field 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 P(x_1,…,x_86) with integer coefficients whether the equation P(x_1,…,x_86)=0 has solutions with x_1,…,x_86∈ℚ.
ER -