| Schur数推广及＂Schur-Pythagoras数＂研究 |
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| 引用本文： | 孙玉芹,刘建军,刘颖.Schur数推广及＂Schur-Pythagoras数＂研究[J].新乡学院学报(自然科学版),2011(6):481-484. |
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| 作者姓名： | 孙玉芹 刘建军 刘颖 |
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| 作者单位： | 上海电力学院数理学院;新乡学院现代教育技术中心;上海立信会计学院数学与信息学院 |
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| 基金项目： | 上海市自然科学基金项目(10ZR1412500;11ZR1425100);上海市教委科研创新项目(11yz241) |
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| 摘 要： | 结合Schur数和勾股数组的特征,推广定义了一类新的临界数,称之为＂Schur-Pythagoras数＂,记作spn.它是最大的自然数,使得自然数集合T={1,2,...,spn}能被划分成n个子集合,在任意子集ST中,方程x2＋y2=z2无解.给出了sp2≥1104及sp2是有限数值还是无穷数值的未解问题的结果.
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| 关 键 词： | Schur数 勾股数组 Schur-Pythagoras |
Generalization of Schur Number and Study of "Schur-Pythagoras Number" |
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| Authors: | SUN Yu-qin LIU Jian-jun LIU Ying |
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| Institution: | 1.College of Mathematics and Physics,Shanghai University of Electric Power,Shanghai 200090,China; 2.Modern Technical Education Center,Xinxiang University,Xinxiang 453003,China; 3.College of Mathematics and Information,Shanghai Lixin University of Commerce,Shanghai 201620,China) |
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| Abstract: | Based on the character of Schur number and Pythagoras array, a new kind of critical value, called ＂Schur-Pythagoras number＂, recorded as sp,, , is generally defined. It is the maximum natural number and makes natural number set T = {1,2,...,spn} be partitioned into n subsets. The equation x2 ＋y2= z2 has no solution in any subset S c T. The result of an unsolved problem is given, that whether sp2 ≥1 104 and sp2 is finite or infinite. |
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| Keywords: | Schur number Pythagoras array Schur-Pythagoras |
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