Fibonacci sequence and Pythagorean triples in the composition of functions for integer solutions from certain operator

TL;DR

This paper explores how Fibonacci sequences and Pythagorean triples can be used to construct functions that generate integer solutions to quadratic equations, linking number theory with calculus applications.

Contribution

It introduces a novel approach using Fibonacci and Pythagorean properties to derive functions for solving specific quadratic equations with integer solutions.

Findings

Theorems establishing connections between Fibonacci numbers, Pythagorean triples, and quadratic solutions.

Demonstrations of functions generating integer solutions to quadratic equations.

Potential applications in number theory and calculus.

Abstract

The following article summarizes research where theorems and their respective demonstrations are postulated based on quadratic equations with special properties given by the Pythagorean triplets and the Fibonacci sequence given the second order of equations where integer solutions are found an environment in number theory and its applications to calculus.