On the \((s,t)\)-Fibonacci and Fibonacci Matrix Sequences

Abstract

It is always fascinating to see what results when seemingly different areas of mathematics overlap. This article reveals one such result; number theory and linear algebra are intertwined to yield complex factorizations of the classic Fibonacci, Pell, Jacobsthal, and Mersenne numbers. Also, in this paper we define a new matrix generalization of the Fibonacci numbers, and using essentially a matrix approach we show some properties of this matrix sequence.