# Volume 13, 2007, Number 2

**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 An integer structure (IS) of the sum (*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

In a series of papers, starting with ⟦1⟧, we discuss new types of Pascal’s like triangles. Triangles from the present form, but not with the present sense, are described in different publications, e.g. ⟦2, 4, 6⟧, but at least the author had not found a research with similar idea. In the second part of our research we shall study properties of some “special” sequences.

**Some ***q*-series inversion formulae

*Original research paper. Pages 15—18*

A. G. Shannon

Full paper (37 Kb) | Abstract

This paper considers some *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

Frey elliptic curves are the curves *y*^{2} = *x*^{3} − *n*^{2}*x* and in this work the group structure *E*(*F*_{P}) of these curves over finite fields *F*_{P} is considered.

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