**Volume 13** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4

**Arithmetical function characterizations and identities induced through equivalence relations**

*Original research paper. Pages 1–19*

Temba Shonhiwa

Full paper (6018 Kb) | Abstract

*A*denote the set of arithmetic functions and ∗ Dirichlet convolution. The paper presents and alternative approach to the study of arithmetic functions by introducing a homomorphism between the subgroup <

*U*, ∗> of the group of units in <

*A*, ∗> and the quotient ring induces through an equivalence relation. The same notion is extended to the case of unitary convolution.

**On some Pascal’s like triangles. Part 3**

*Original research paper. Pages 20–26*

Krassimir T. Atanassov

Full paper (87 Kb) | Abstract

In the first part of our research we studied properties of some standard sequences and in the second part – of some “special” sequences. Now, we shall construct (0, 1)-analogous of the Pascal’s like triangles (or “(mod 2)-triangles”) from the both previous papers, i.e., we will construct (mod 2)-values of their elements and will discuss the obtained configurations. We will call the new triangles “(0, 1)-triangles”.

**Modular-ring class structures of x^{n} ± y^{n}**

*Original research paper. Pages 27–35*

J. V. Leyendekkers and A. G. Shannon

Full paper (355 Kb) | Abstract

*x*and

*y*. For instance, the sum of two identical powers,

*m*, cannot form primes when

*m*is odd or when

*m*is even if the powers are odd and of the form

*m*/2. The expanded forms of the factors indicate why the structure acts against the sum ever equalling an identical power. The difference of odd powers can yield primes when

*x*−

*y*= 1. The difference of even powers cannot yield primes whereas the sum can when

*m*/2

*is even. However,*

^{n}*x*

^{2}−

*y*

^{2}can equal a prime when

*x*−

*y*= 1.

**Remark on Jacobsthal numbers**

*Original research paper. Page 36*

Krassimir T. Atanassov

Full paper (83 Kb)