An equation involving the F.Smarandache multiplicative function SM(n).(Report) Scientia Magna | January 1, 2008| | COPYRIGHT 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) Copyright

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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