Linear difference equations and Fibonacci structures

G. E. Deev^a, S. V. Ermakov^a, S. Starkloff<sup>b

a</sup> Obninsk Institute for Nuclear Power Engineering, National Research Nuclear University MEPhI, Obninsk, Russian Federation
^b University of Basel, Basel, Switzerland

Abstract: We studied the solution of linear difference equations of arbitrary order and demonstrated that they can be expressed using the Fibonacci structure, which we defined in the course of our presentation. This structure, which consists of number sequences related to the classical Fibonacci numbers, is of independent interest. Each sequence in the structure has an associated Phidias number. In this paper, we present several results on the properties of the Fibonacci structure and Phidias numbers.

Keywords: difference equations, Fibonacci numbers, Phidias numbers.