**Volume 16** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4

**Equations for primes obtained from integer structure**

*Original research paper. Pages 1—10*

J. V. Leyendekkers, A. Shannon

Full paper (PDF, 224 Kb) | Abstract

*R*

_{1}+ 1 are equal to a sum of squares. Such primes are in Class ̅1

_{4}⊂ Z

_{4}, a modular ring. The rows of squares in Z

_{4}are well defined and this permits equalities for the primes to be derived from the integer structure. These equalities have the forms

*R*

_{1}=

*r*

_{1}+

*r*

_{0}where

*r*

_{1}= 3

*n*(3

*n*± 1) or 2 + 9n′(n′ + 1) and

*r*

_{0}= 2

^{2q}(12

*m*(3

*m*± 1) + 1) or 2

^{2q}(4(2 + 9

*m*′(

*m*′ + 1)) + 1), with

*q*= 0, 1, 2, 3,… and

*n*,

*m*yielding the pentagonal numbers, and

*n*′,

*m*′ the triangular numbers. When

*n*=

*m*the equations are similar to Euler’s prime equation. Equations for the remaining primes, in Class ̅3

_{4}may be obtained in the same manner using

*p*=

*y*

^{2}−

*x*

^{2}with (

*y*−

*x*) = 1.

**Another generalization of the Fibonacci and Lucas numbers**

*Original research paper. Pages 11—17*

A. Shannon

Full paper (PDF, 136 Kb) | Abstract

**Some results on infinite power towers**

*Original research paper. Pages 18—24*

Mladen Vassilev-Missana

Full paper (PDF, 223 Kb) | Abstract

**Note on φ, ψ and σ-functions. Part 2**

*Original research paper. Pages 25—28*

Krassimir Atanassov

Full paper (PDF, 125 Kb) | Abstract

*φ*,

*ψ*and

*σ*is being discussed and illustrated.