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Article: One problem related to the Smarandache function.(Report)
- Article from:
- Scientia Magna
- Article date:
- September 1, 2008
- Author:
CopyrightCOPYRIGHT 2008 American Research Press. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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Abstract For any positive integer n, the famous F. Smarandache function S(n) is defined as the smallest positive integer m such that n | m!. That is, S(n) = min {m : n | m!, n [member of] N}. The main purpose of this paper is using the elementary method to study the number of the solutions of the congruent equation [1.sup.s(n-1)] + [2.sup.s(n-1)] + ... + [(n-1).sup.s(n-1)] + 1 [equivalent to] 0 (mod n), and give its all prime number solutions.
Keywords F. Smarandache function, divisibility, primitive root.
[section] 1. Introduction and result
For any positive integer n, the famous F. Smarandache function S(n) is defined as the smallest positive ...