On the exponential Diophantine equation (22m+1−1)+(13)n=z2

Nowadays, scholars are very interested to determine the solution of different Diophantine equations because these equations have numerous applications in the field of coordinate geometry, cryptography, trigonometry and applied algebra. These equations help us for finding the integer solution of famous Pythagoras theorem and Pell’s equation. Finding the solution of Diophantine equations have many challenges for scholars due to absence of generalize methods. In the present paper, author studied the exponential Diophantine equation ( 2 2 m + 1 − 1 ) + ( 13 ) n = z 2 , where m , n are whole numbers, for its solution in whole numbers. Results show that the exponential Diophantine equation ( 2 2 m + 1 − 1 ) + ( 13 ) n = z 2 , where m , n are whole numbers, has no solution in whole number.