Monotonicity of solutions to second order linear difference equations with constant coefficients

TL;DR

This paper investigates the monotonic behavior of solutions to second order linear difference equations with constant coefficients and uses these properties to characterize Fibonacci numbers.

Contribution

It provides new insights into the monotonicity of solutions and offers a novel characterization of Fibonacci numbers based on these properties.

Findings

Solutions exhibit specific monotone behaviors under certain conditions.

Fibonacci numbers can be characterized by the monotonicity properties of related difference equations.

Abstract

We describe some monotone properties of solutions to second order linear difference equations with real constant coefficients. As an application, we give a characterization of the Fibonacci numbers.