Factors of composite $4n^2 +1$ using Fermat's factorization method

TL;DR

This paper explores the factorization of numbers of the form 4n^2+1 using Fermat's method, characterizing their factors and analyzing composite Fermat numbers.

Contribution

It introduces a characterization of all proper factors of 4n^2+1 and applies Fermat's factorization to these specific composite numbers.

Findings

Proper factors of 4n^2+1 are characterized in terms of their form

Fermat's factorization method effectively factors these numbers

Analysis of composite Fermat numbers included

Abstract

In this article, we factor the composite $4n^2 +1$ using Fermat's factorization method. Consequently, we characterized all proper factors of composite $4n^2 +1$ in terms of its form. Furthermore, the composite Fermat's number is considered in this study.