Generalized Fibonacci Primitive Roots

TL;DR

This paper extends the concept of Fibonacci primitive roots to all integers and provides an asymptotic formula for counting how many integers possess such roots.

Contribution

It introduces a generalization of Fibonacci primitive roots to integers and derives an asymptotic counting formula.

Findings

Derived an asymptotic formula for counting integers with Fibonacci primitive roots.

Generalized Fibonacci primitive roots from primes to all integers.

Provides theoretical foundation for further research in primitive roots.

Abstract

This note generalizes the Fibonacci primitive roots to the set of integers. An asymptotic formula for counting the number of integers with such primitive root is introduced here.