This article re-considers some interrelations among Pythagorean triads and various Fibonacci identities and their generalizations, with some accompanying questions to provoke further development by interested readers or their students. (Contains 3 tables.)

Analysis of integer structure and right-end-digits can illustrate why 3 and 5 are features of primitive Pythagorean triples. The results also utilize the triangular and pentagonal numbers. (Contains 5 tables.)

A base for linear recursive sequences, such as the sequence of Fibonacci numbers, is defined within the framework of the sum of the digits of a number. Examples of bases of a number of such sequences are then outlined, and a Mobius strip is also used to illustrate the effects diagrammatically.

Some infinite series are analysed on the basis of the hypergeometric function and integer structure and modular rings. The resulting generalized functions are compared with differentiation of the "mother" series. (Contains 1 table.)

This paper aims to explore some properties of certain third-order linear sequences which have some properties analogous to the better known second-order sequences of Fibonacci and Lucas. Historical background issues are outlined. These, together with the number and combinatorial theoretical results, provide plenty of pedagogical opportunities for…

An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.

Biotechnological processes (BTP) are characterized by a complicated structure of organization and interdependent characteristics. Partial differential equations or systems of partial differential equations are used for their behavioural description as objects with distributed parameters. Modelling of substrate without regard to dispersion…

The modular ring Z[subscript 6] defines integers via ( 6r[subscript i] + ( i - 3)) where i is the class and r[subscript i] the row when tabulated in an array. Since only Classes 2[subscipt 6] and 4[subscript 6] contain odd primes, this modular ring is ideally suited to the analysis of twin primes. The calculations are facilitated by the use of the…

Using the modular ring Zeta[subscript 4], simple algebra is used to study diophantine equations of the form (x[cubed]-a=y[squared]). Fermat challenged his contemporaries to solve this equation when a = 2. They were unable to do so, although Fermat had devised a rather complicated proof himself. (Contains 2 tables.)

This note explores ways in which the Fibonacci numbers can be used to introduce difference equations as a prelude to differential equations. The rationale is that the formal aspects of discrete mathematics can provide a concrete introduction to the mechanisms of solving difference and differential equations without the distractions of the analytic…

The authors report on the stage of a project (tertiary education in applied mathematics, TEAM) aimed at investigating first-year students' expectations and preferences and lecturers' aims in relation to first-year undergraduate mathematics courses. (Author/MN)

The educational and statistical validity of grading schemes is often open to question when multiple evaluation techniques are used. A method of scaling is proposed and discussed in relation to normal scores. (SD)

This paper describes an approach to the problem of teaching first-year tertiary level mathematics students who have widely varying levels of achievement and ability in mathematics. The evaluation of some aspects of the proposed solution to the problem is based on a semantic differential and a Likert-type questionnaire. (Author/MK)

The semantic differential--one approach to attitude measurement--basically records a combination of a person's associations with a particular concept with a scaling procedure. This paper considers the implications of such a device for teachers of mathematics. (Author/MK)