Review on Number Theory & Various Integer Solutions within Algebraic Equations

Abstract

This paper explores the historical evolution and modern advancements in number theory, focusing on the development and solutions of Various integer solutions within algebraic equations. Number theory, often referred to as the "Queen of Mathematics," has its roots in ancient civilizations and continues to inspire research in both theoretical and applied mathematics. Various integer solutions within algebraic equations, named after the Greek mathematician Diophantus, are a central theme, requiring solutions in integers or rational numbers.