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

**A note on rhotrix exponent rule and its applications to some special series and polynomial equations defined over rhotrices**

*Original research paper. Pages 1—15*

A. Mohammed

Full paper (138 Kb) | Abstract

**Odd powers as sums of squares**

*Original research paper. Pages 16—24*

J. V. Leyendekkers and A. G. Shannon

Full paper (113 Kb) | Abstract

*n*can equal a sum of squares only if the integers are in Class ̅1

_{4}of the Modular Ring Z

_{4}. The primes raised to an odd power are unique in that they only have (

*n*− 1) square couples. These couples depend on the single couple (

*a*

_{1},

*b*

_{1}). A general equation is given for predicting the square couples of

*p*and odd-powered composites. Even integers raised to an odd power have no primitive solutions for such square couples, because the sum of two odd squares falls in Class ̅2

^{n}_{4}where there are no powers at all.

**Some generalized rising binomial coefficients**

*Original research paper. Pages 25—30*

A. G. Shannon

Full paper (95 Kb) | Abstract

**On some Pascal’s like triangles. Part 1**

*Original research paper. Pages 31—36*

Krassimir T. Atanassov

Full paper (103 Kb) | Abstract