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

**Integer structure analysis of primes and composites from sums of two fourth powers**

*Original research paper. Pages 1—9*

J. V. Leyendekkers and A. G. Shannon

Full paper (131 Kb) | Abstract

*x*

^{4}+

*y*

^{4}) is done using the modular ring Z

_{6}. This sum generated many primes and the row structure of such primes is explored. The class functions of the composite factors of this sum are also given, and these, together with the associated row functions, illustrate why it is impossible to produce an integer to the fourth power from such sums. The overall results are consistent with those previously found with IS analysis.

**On some Pascal’s like triangles. Part 2**

*Original research paper. Pages 10—14*

Krassimir T. Atanassov

Full paper (87 Kb) | Abstract

**Some q-series inversion formulae**

*Original research paper. Pages 15—18*

A. G. Shannon

Full paper (37 Kb) | Abstract

*q*-extensions of binomial coefficients formed from rising factorial coefficients. Some of the results are applied to a Möbius Inversion Formula based on extensions of ideas initially developed by Leonard Carlitz.

**The group structure of Frey elliptic curves over finite fields F_{P}**

*Original research paper. Pages 19—24*

Nash Yıldız İkikardeş, Musa Demirci, Gökhan Soydan and İsmail Naci Cangül

Full paper (2795 Kb) | Abstract

*y*

^{2}=

*x*

^{3}−

*n*

^{2}

*x*and in this work the group structure

*E*(

*F*) of these curves over finite fields

_{P}*F*is considered.

_{P}This group structure and the number of points on these elliptic curves depend on the existence of elements of order 4. Therefore the cases where the group of the curve has such elements are determined. It is also shown that the number of such elements, if any, is either 4 or 12. Classification is made according to

*n*is a quadratic residue or not.

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