IJPAM: Volume 14, No. 2 (2004)

ON EQUATIONS INVOLVING THE NUMBER
OF REDUCIBLE ELEMENTS IN $Z_{n}$

Badrié Kojok$^1$, A.N. El-Kassar$^2$
$^1$Department of Mathematics
Faculty of Engineering
University Saint Joseph
P.O. Box 514, Mar Roukos, Beirut, LEBANON
e-mail: badrie.kojok@fi.usj.edu.lb
$^2$Department of Mathematics
Faculty of Sciences
Beirut Arab University
P.O. Box 11-5020, Beirut, LEBANON
e-mail: ak1@bau.edu.lb


Abstract.The purpose of this paper is to study equations involving two new number theoretic functions, the number of irreducible elements in $Z_{n}$ and the number of reducible elements in $Z_{n}$. Complete characterizations of many of these equations are given using properties of these new functions while partial results for other equations are obtained.

Received: April 22, 2004

AMS Subject Classification: 11A25, 16U30

Key Words and Phrases: number-theoretic equations, divisibility, irreducible elements

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 14
Issue: 2