中文摘要：

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ST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.

英文摘要：

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.