Examining Prime Numbers/Components of Diophantine D(∓3) Sets

Authors : Özen Özer

Pages : 566-579

Doi:10.47495/okufbed.1535231

View : 33 | Download : 43

Publication Date : 2025-03-12

Article Type : Research Paper

Abstract :Mathematicians have long been interested in Diophantine sets. They have good ways to analyze the calculations and results. The aim of this paper is to explore the enigmatic world of diophantine D( ∓3) set shapes, revealing a new emphasis on its complex specifications and deep correlations. The Diophantine D( ∓3) sets, defined as integer values in this work, represent significant domain ripe for examinations. Our study analyzes these sets in detail, ignoring their cardinals, and aims to reveal hidden patterns and unique characteristics. By scrutinizing their structure, our intention is to reveal the high mathematics content of these collections. In our discussion we highlight basic principles of basic algebraic number theory, invoking the law of quadratic reciprocity, Diophantine equations, and the enduring grace of major mathematicians like Gauss, Dirichlet and Fermat. These tools and logic serve as viewers of our discussion, ultimately Diophantine provides a deeper appreciation of the concepts in the D( ∓3) sets and their importance in the broader mathematical terrain.
Keywords : Diophantine Denklemleri, Sylvester, Gauss’un ve Eisenstein’in Lemması, İkinci Dereceden Karşılıklılık Yasası, Modüler Hesaplama ve Diophantine Kümeleri, Legendre Sembolü ve İkinci Dereceden Kalanlar.