# Fibonacci Sequences And Real Quadratic p-Rational Fields

## TL;DR

This paper investigates the p-rationality of real quadratic fields by examining generalized Fibonacci numbers and their periodic behavior modulo integers, offering new insights into number theory properties.

## Contribution

It introduces a novel approach linking Fibonacci sequences to the p-rationality of real quadratic fields, expanding understanding of their algebraic structure.

## Key findings

- Established criteria connecting Fibonacci periods to p-rationality
- Identified patterns in Fibonacci sequences relevant to quadratic fields
- Provided new characterizations of p-rational real quadratic fields

## Abstract

We study the p-rationality of real quadratic fields in terms of generalized Fibonacci numbers and their periods modulo positive integers.