An equation involving the F.Smarandache multiplicative function SM(n).(Report)

From: Scientia Magna | Date: January 1, 2008| Author: | Copyright information

Abstract For any positive integer n > 1, let n = [P.sup.[alpha]1.sub.1][P.sup.[alpha]2.sub.2] ...[P.sup.[alpha]kappa.sub.kappa] be the fractorization of n into prime powers. The famous F.Smarandache multiplicative function SM(n) is defined as SM(n) = max{[[alpha].sub.1], [P.sub.1], [[alpha].sub.2] [P.sub.2], ... [[alpha].sub.kappa]}. Euler function [empty set] (n) denotes the number of all positive integers not exceeding n which are relatively prime to n. The main purpose of this paper is using the elementary method to study all positive integer solutions of the equation ...

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