Inherent Approaches to Solving Exponential Diophantine Equations involving Disarium Numbers of order 2 to 4.

Abstract

Exponential Diophantine equations, which involve integer solutions to equations containing variables in exponents, represent a significant area of study in number theory. In this article, we explore, we introduce three distinct exponential Diophantine equations. By incorporating insights from the Catalan Conjecture and utilizing Disarium numbers of orders 2, 3, and 4, we establish non-negative integer solutions to these equations. A series of numerical examples is also presented to validate the proposed method and demonstrate how the equations can be effectively solved.