On the back concatenated square sequence

摘要：

For any positive integer n, the famous Smarandache concatenated square sequence a(n) is defined as the positive integer a(n)=122232… (n 1)2n2, and the Smarandache back concatenated square sequence b(n) is defined as the positive integer b(n) = n2(n -1)2(n 2)2…42322212. For example, the first few terms of a(n) are: 1, 14, 149, 14925,1492536, ……. The first few terms of b(n) are 1, 41, 941, 16941, 2516941, ……. In reference 2, Professor F.Smarandache asked us to study such a problem: How many perfect square number are there in the sequence a(n) and b(n)? The main purpose of this paper is using the elementary methods to study this problem, and prove that there is only one perfect square number 1 in the Smarandache back concatenated square sequence b(n). This solved a problem proposed by Smarandache in his book 2.

关键词： Concatenated square sequence back concatenated square sequence perfect square.

作者: Ling Li

作者单位: Department of Mathematics, Northwest University, Xian, Shaanxi, P.R.China Basic Courses Department, Shaanxi Polytechnic Institute, 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: 90-91

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）