Volume 13, 2007, Number 2

An integer structure (IS) of the sum (x⁴ + y⁴) is done using the modular ring Z₆. 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.

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.

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.