# On the regular elements in Zn

## Related Articles

- On the regular elements in Zn. Alkam, Osama; Osba, Emad Abu // Turkish Journal of Mathematics;2008, Vol. 32 Issue 2, p31
All rings are assumed to be finite commutative with identity element. An element a Ïµ R is called a regular element if there exists b Ïµ R such that a = a2b, the element b is called a von Neumann inverse for a. A characterization is given for regular elements and their inverses in â„¤n,...

- THE AVERAGE NUMBER OF SOLUTIONS OF THE DIOPHANTINE EQUATION U2 + V2 = W3 AND RELATED ARITHMETIC FUNCTIONS. K�hleitner, M.; Nowak, W. G. // Acta Mathematica Hungarica;2004, Vol. 104 Issue 3, p225
For the number of integer solutions of the title equation, with W ? x (x a large parameter), an asymptotics of the form Ax log x + Bx + O(x1/2(log x)ï¿½(log log x)ï¿½) is established. This is achieved in a general setting which furnishes applications to some other natural arithmetic functions.

- ACTIONS OF ARITHMETIC FUNCTIONS ON MATRICES AND CORRESPONDING REPRESENTATIONS. CHO, ILWOO; JORGENSEN, PALLE // Annals of Functional Analysis;2014, Vol. 5 Issue 2, p90
In this paper, we study a class of representations of arithmetic functions, and corresponding operator-theoretic and free probabilistic properties. We associate given arithmetic functions f to certain matrices Î±n(f).

- A short interval result for the exponential divisor function. Shuqian Gao; Qian Zheng // Scientia Magna;2010, Vol. 6 Issue 3, p15
An integer d = ?si=1 pbii is called the exponential divisor of n = ?si=1 paii > 1 if bijai for every i ? {1, 2, ï¿½, s}. Let t (e)(n) denote the number of exponential divisors of n, where t(e)(1) = 1 by convention. The aim of this paper is to establish a short interval result for for...

- Short interval asymptotics for a class of arithmetic functions. Garaev, M. Z.; Luca, F.; Nowak, W. G. // Acta Mathematica Hungarica;Oct2006, Vol. 113 Issue 1/2, p85
We provide a general asymptotic formula which permits applications to sums like ["Multiple line equation(s) cannot be represented in ASCII text"]. where d(n) and r(n) are the usual arithmetic functions (number of divisions, sums of two squares), and y is small compared to x.

- Germain, Sophie (Marie) (1776 - 1831). // Hutchinson Dictionary of Scientific Biography;2005, p1
French mathematician who developed the modern theory of elasticity (the mathematical theory of the stress and strain that a material can sustain and still return to its original form) and made major contributions to numbers theory and acoustics.

- Fast mining of distance-based outliers in high-dimensional datasets. Ghoting, Amol; Parthasarathy, Srinivasan; Otey, Matthew Eric // Data Mining & Knowledge Discovery;Jun2008, Vol. 16 Issue 3, p349
Defining outliers by their distance to neighboring data points has been shown to be an effective non-parametric approach to outlier detection. In recent years, many research efforts have looked at developing fast distance-based outlier detection algorithms. Several of the existing distance-based...

- RANK EQUALITIES FOR MOORE-PENROSE INVERSE AND DRAZIN INVERSE OVER QUATERNION. HUASHENG ZHANG // Annals of Functional Analysis;2012, Vol. 3 Issue 2, p115
In this paper, we consider the ranks of four real matrices Gi(i = 0; 1; 2; 3) in M, where M = M0+M1i+M2j+M3k is an arbitrary quaternion matrix, and My = G0 + G1i + G2j + G3k is the Moore-Penrose inverse of M. Similarly, the ranks of four real matrices in Drazin inverse of a quaternion matrix are...

- The "ABC" Conjecture for p-Adic Entire Functions of Several Variables. Vu Hoai An; Doan Quang Manh // Southeast Asian Bulletin of Mathematics;2004, Vol. 27 Issue 6, p959
We show that the analogue of "abe" conjecture for p-adic entire functions in several variables is true.