On a problem of the Schur

摘要：

For any positive integer n, let r be the positive integer such that the set 1, 2, …, r can be partitioned into n classes, and no any class contain integers x, y, z with xy=z. In reference 1 (See Problem 57), Schur asked us to find the maximum r. In this paper, we use the elementary methods to study this problem, and give a sharp lower bound estimates for r.

关键词： Schurs problem partition lower bound.

作者: Yani Zheng

作者单位: Department of Mathematics, Northwest University, Xian, Shaanxi, P.R.China Department of Mathematics, Xianyang Normal College, Xianyang, Shaanxi, P.R.China

会议类型: 国际会议

会议名称: The Fourth International Conference on Number Theory and Smarandache Problems(第四届国际数论与Smarandache问题学术会议)

会议地点: 西安

会议语种:英文

页码: 1-2

在线出版日期: 2008-03-21（万方平台首次上网日期，不代表论文的发表时间）