On the Smarandache pierced chain

摘要：

If n≥1, then c(n) = 101 × (104n-4+104n-8+…+104+1) is called as the Smarandache Pierced Chain. Its first few terms are:101, 1010101, 10101010101, 101010101010101, 1010101010101010101,……In reference 2, Dr.Kashihara Kenichiro asked whether c(n)/101 is a square-free number for all n≥2? The main purpose of this paper is using the elementary method to study this problem,and prove that there are infinite positive integers n such that 9 divides c(n)/101. That is to say,c(n)/101 is not a square-free number for infinite integers n≥2.

关键词： Smarandache Pierced Chain square-free number sequence.

作者: Su Gou Jianghua Li

作者单位: Department of Applied Mathematics and Physics Xian Institute of Posts and Telecommunications, Xian Department of Mathematics,Northwest University,Xian,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: 44-45

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）