发表机构
School of Mathematics, Nanjing University（南京大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文改进了希尔伯特第十问题的相关结论，证明不存在算法可判定含十个未知数的整数系数多项式方程是否有整数解。
AI 中文摘要
整数上的希尔伯特第十问题于1970年由Y. Matiyasevich给出否定解答。本文证明，不存在算法可判定任意具有整数系数和十个未知数的多项式方程$P(z_1,\ldots,z_{10})=0$是否存在整数解，这改进了此前的十一个未知数定理。
英文摘要
Hilbert's Tenth Problem over the integers was solved negatively by Y. Matiyasevich in 1970. In this paper, we prove that there is no algorithm to determine for any polynomial equation $P(z_1,\ldots,z_{10})=0$ (with integer coefficients and ten unknowns) whether it has integer solutions. This improves the previous 11 unknowns theorem.
Comments15 pages. Correct few typos
