Some properties of Fibonacci primes

TL;DR

This paper characterizes Fibonacci primes of specific quadratic forms using combinatorics and number theory, and evaluates certain distances related to Fibonacci numbers and functions.

Contribution

It introduces new characterizations of Fibonacci primes of particular quadratic forms and analyzes distances associated with Fibonacci numbers.

Findings

Characterization of Fibonacci primes of the form x^2 + r y^2

Evaluation of distances related to Fibonacci numbers

Application of combinatorics and number theory techniques

Abstract

In this article we charaterize the primes Fibonacci numbers of the form $x^2 +ry^2$, where $r = 1,$ $r$ is a prime positive integer number or r is a power of a prime positive integer, using techniques of combinatorics and numbers theory. We also evaluate some distances related to the Fibonacci numbers and function.