Author(s)

Md. Al-Amin Khan, Abdur Rashid, Md. Sharif Uddin

Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh.

In this paper, we study two Diophantine equations of the type p^x + 9^y = z² , where p is a prime number. We find that the equation 2^x + 9^y = z² has exactly two solutions (x, y, z) in non-negative integer i.e., {(3, 0, 3),(4, 1, 5)} but 5^x + 9^y = z² has no non-negative integer solution.

Exponential Diophantine Equation, Integer Solutions

Khan, M. , Rashid, A. and Uddin, M. (2016) Non-Negative Integer Solutions of Two Diophantine Equations 2^x + 9^y = z² and 5^x + 9^y = z². Journal of Applied Mathematics and Physics, 4, 762-765. doi: 10.4236/jamp.2016.44086.