Exponential Diophantine Equations Concerning Numbers in Reverse Order

Abstract

In this scholarly article, we delve into the intricate realm of exponential Diophantine equations, specifically those pertaining to the reversal of digits denoted by \(29^x+92^y=z^2, \quad 38^x+83^y=z^2, \quad 47^x+74^y=z^2, \quad 56^x+65^y=z^2\). Within this context, to determine if a distinct solution exists for the considered exponential equation, it is finally revealed that it has infinitely many solutions, but all of the aforesaid exponential equations have a similar solution, identified as \((1,1,11)\).