**Volume 19** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4

**On the theorem of Conrey and Iwaniec**

*Original research paper. Pages 1—9*

Jeffrey Stopple

Full paper (PDF, 177 Kb) | Abstract

** Method of infinite ascent applied on A^{3} ± nB^{2} = C^{3}**

*Original research paper. Pages 10*

*—*14Susil Kumar Jena

Full paper (PDF, 124 Kb) | Abstract

*A*

^{3}±

*nB*

^{2}=

*C*

^{3}will generate infinite number of co-prime integral solutions for (

*A*,

*B*,

*C*) for any positive integer

*n*.

** Two-term Egyptian fractions**

*Original research paper. Pages 15 —25*

Tieling Chen and Reginald Koo

Full paper (PDF, 190 Kb) | Abstract

*m/n*where each prime factor

*p*of

*n*satisfies

*p*≡ ±1 (mod

*m*): necessary and sufficient conditions for the existence of proper two-term Egyptian fraction expressions of such

*m*/

*n*are given, together with methods to find these representations. Furthermore, we determine the number of proper two-term Egyptian fraction expressions for 1

*/m*, 2

*/m*, 3

*/m*, 4

*/m*and 6

*/m*.

** Short remark on Möbius function**

*Original research paper. Pages 26 —29*

Krassimir T. Atanassov

Full paper (PDF, 119 Kb) | Abstract

*μ*are introduced, and illustrated with an example.

** Extension of factorial concept to negative numbers**

*Original research paper. Pages 30 —42*

A. M. Ibrahim

Full paper (PDF, 125 Kb) | Abstract

*n*! to negative numbers –

*n*! is introduced. Based on this extension, a formulation of specific generalization cases for different forms of negative factorials are analyzed and presented.

** Note on some explicit formulae for twin prime counting function**

*Original research paper. Pages 43 —48*

Mladen Vassilev-Missana

Full paper (PDF, 144 Kb) | Abstract

(where π

_{2}denotes the twin prime counting function and φ is Euler’s totient function) is established. Also for any integer n ≥ 5 the formula

(where f is arbitrary artihmetic function with strictly positive values satisfying the condition

is proved.

** Fibonacci and Lucas primes**

*Original research paper. Pages 49 —59*

J. V. Leyendekkers and A. G. Shannon

Full paper (PDF, 132 Kb) | Abstract

*F*, formed when n equals a prime, p, are analysed using the modular ring

_{n}*Z*

_{5}, Pascal’s Triangle as well as various properties of the Fibonacci numbers to calculate “Pascal-Fibonacci” numbers to test primality by demonstrating the many structural differences between the cases when

*F*is prime or composite.

_{n}** On the mean values of Dedekind sums over short intervals**

*Original research paper. Pages 60 —68*

Weixia Liu

Full paper (PDF, 167 Kb) | Abstract

** Generalization of a few results in integer partitions**

*Original research paper. Pages 69 —76*

Manosij Ghosh Dastidar and Sourav Sen Gupta

Full paper (PDF, 171 Kb) | Abstract

** Note on Legendre symbols connecting with certain infinite series**

*Original research paper. Pages 77 —83*

Ramesh Kumar Muthumalai

Full paper (PDF, 143 Kb) | Abstract