On The Generalized Multiplicative Euler Phi Function

Abstract

The generalized group of units of the ring modulo $n$ was first introduced by El-Kassar and Chehade, written as $U^k(Z_n)$. This allows us to formulate a new generalization to the Euler phi function $\phi (n)$, that represents the order of and it is denoted by ${\phi }^k(n).$ In this paper, we introduce this newly defined function, where we compute its explicit form and examine some of its properties similar to that of $\phi (n)$. In addition, we study some generalized equations involving ${\phi }^k(n)$ where complete solution is given for some equations by considering the general case and others for some particular cases.

References in corpus (1)

• On the Structure of the Generalized Group of Units