Abstract

Polynomial equations with integer solutions, or diophantine equations, are a set of equations with wide applications in many different fields. This essay investigates the practical uses of Diophantine equations in areas like number theory, network traffic flow, corporate investment, and chemical equation balance. It also looks at the historical evolution of these equations (see [4-5]). We show how useful Diophantine equations are for solving real-world issues requiring integer solutions by examining both linear and non-linear versions of the equation. The importance of these equations for both theoretical mathematics and practical applications is demonstrated by highlighting well-known outcomes such Pythagorean triples and Fermat's Last Theorem. In order to address difficult problems in real-world circumstances and simplify them, the study intends to emphasize the significance of Diophantine equations