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

**Unit coefficient sums for certain Morgan–Voyce numbers**

*Original research paper. Pages 117—127*

A. F. Horadam

Full paper (PDF, 328 Kb) | Abstract

**Analysis of odd exponent triples within the modular ring ℤ _{4} using binomial expansions and Fermat reductions**

*Original research paper. Pages 128—158*

J. V. Leyendekkers, J. M. Rybak and A. G. Shannon

Full paper (PDF, 967 Kb) | Abstract

_{4}in order to analyse why odd powered triples with exponents greater than unity cannot exist in integer form. Two methods are given which exploit old expansion and reduction techniques in a new way. By way of conclusion the second method is also illustrated by reference to Pythagorean triples.

**On certain arithmetic products involving regular convolutions**

*Original research paper. Pages 159—166*

László Tóth and József Sándor

Full paper (PDF, 364 Kb) | Abstract

**Note on two inequalities**

*Original research paper. Pages 167—169*

Mladen Vassilev and Krassimir Atanassov

Full paper (PDF, 113 Kb)

**A partial difference equation and a minimal surface**

*Original research paper. Pages 170—172*

J. H. Clarke and A. G. Shannon

Full paper (PDF, 216 Kb) | Abstract

(1 + u_{i,j+i}^{2} − 2u_{i,j}u_{i,j+1} + u_{i,j}^{2})(u_{i+2,j} − 2u_{i+1,j} + u_{i,j}) − 2((u_{i+1,j} − u_{i,j}) u_{i,j+1} − (u_{i+l,j} − u_{i,j}) u_{i,j})

+ (l + u_{i+1,j}^{2} − 2u_{i+l,j}u_{i,j} + u_{i,j}^{2})(u_{i,j+2} − 2u_{i,j+1} + u_{i,j}) = 0.

The purpose of this note it to convert this difference equation into the corresponding partial differential equation and to examine the resulting minimal surface. This is done formally without digressing into the issues associated with mapping from the integers to the reals.

**The modular ring Z _{6} and the area of a Pythagorean triangle**

*Original research paper. Pages 173—175*

J. V. Leyendekkers, J. M. Rybak and A. G. Shannon

Full paper (PDF, 89 Kb) | Abstract

_{6}[1] to obtain the same result.