SOLUTION OF THE EXPONENTIAL DIOPHANTINE EQUATION 10^X + 400^Y=Z^2

Abstract

Diophantine equations are so important in solving important real-world problems like network flow problems, pole placement problems, business investment problems, and data privacy problems that researchers are becoming more interested in developing new techniques for analyzing the nature and solutions of the various Diophantine equations. In the present study, authors examined the Diophantine equation〖10〗^X+〖400〗^Y=Z^2, where X,Y,Zare non-negative integers, for the non-negative integer solution of this equation. A result of the present study shows that it has no non-negative integer solution.