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- Title
An equation involving Smarandache function S(n) and pseudo Smarandache function Z<sub>1</sub> (n) and its positive integer solutions.
- Authors
CHE Shun
- Abstract
For any positive integer n, the famous Smarandache function S(n) defined as the smallest positiveinteger m such that n|m!. That is, S(n) = min {m: m ∈ N, n | m!}. The pseudo Smarandache function Z1(n) defined as the smallest integer m such that n|m (m+l) (2w+l)/6 or Z1 (n) =min {m:m ∈ N, n| 1² + 2²+...+m²}, where N denotes the set of all positive integers. The solvability of the equation Z1(n) + 1 = S(n) is studied. Using the elementary method, its all positive solutions is given. At the same time, their exact representation of all solutions are given.
- Subjects
SMARANDACHE function; FUNCTIONAL equations; INTEGERS; PROBLEM solving; MATHEMATICAL programming; NUMERICAL analysis
- Publication
Basic Sciences Journal of Textile Universities / Fangzhi Gaoxiao Jichu Kexue Xuebao, 2013, Vol 26, Issue 1, p15
- ISSN
1006-8341
- Publication type
Article