Ramazan Dikici

3-Step Fibonacci series modulo m

We have proved two original theorem concerning Wall number of the the 3-step Fibonacci sequences. We give five conjectures concerning 3-step Fibonacci sequence. Furthermore, we also give a computer verification of those conjectures for the primes less than 5x10^5.

The effect of the 4MAT method (learning styles and brain hemispheres) of instruction on achievement in mathematics

The purpose of this study was to determine the efficiency of 4MAT method of instruction in which learning style and cerebral hemispheres are taken into account in teaching the binary operation and its properties in mathematics. The sample of this study comprised 58 ninth grade students in two separate classes in a high school. One of the classes was selected as the experimental group in which 4MAT method of instruction was used; and the other class was selected as the control group in which the traditional teaching was given, and this selection was performed randomly. The data have been obtained primarily from three scales, namely ‘mathematical knowledge test’, ‘mathematical attitude scale’ and ‘knowledge test on binary operation and its properties’. It has been determined that 4MAT method of instruction was more efficient than the traditional method in teaching of the binary operation subject in mathematics.

An application of Fibonacci sequences in groups

In this work, we have proved that, for the 3-step general Fibonacci recurrence and any finite p-group of exponent p and nilpotency class 2, the length of a fundamental period of any loop satisfying the recurrence must divide the period of the ordinary 3-step general Fibonacci sequence in the field GF(p).

Wall and Vinson Revisited

Let G be a finite group. We define a family of recurrences, parameterized by natural numbers n, via equations

Applications of Fibonacci sequences in a finite nilpotent group

{{x}_{i}} = {{x}_{{i - 1}}}{{x}_{{i - 2}}} \cdots {{x}_{{i - n}}}.

Fibonacci Sequences in Finite Nilpotent Groups

(Rn)

Recurrences in finite groups

We have proved that, for the 2-step general Fibonacci sequence and any finite p-group of exponent p and nilpotency class 3, the length of a fundamental period of any loop constructed by any two generating elements is the same as the period of the ordinary 2-step Fibonacci sequence in the field GF(p).

ON SOME HERMITE-HADAMARD TYPE INEQUALITIES FOR TWICE DIFFERENTIABLE MAPPINGS AND APPLICATIONS

We have proved two original theorem concerning Wall number of the the three-step Fibonacci sequences constructed by three elements of any finite p-group of exponent p and nilpotency class 4.