BibTeX:

@article{IJIRSTV3I9062,
     title={On the Diophantine Equation 128^x + 961^y =z^2},
     author={G. Jeyakrishnan and Dr. G. Komahan},
     journal={International Journal for Innovative Research in Science & Technology},
     volume={3},
     number={9},
     pages={119--120},
     year={},
     url={http://www.ijirst.org/articles/IJIRSTV3I9062.pdf},
     publisher={IJIRST (International Journal for Innovative Research in Science & Technology)},
}

By applying Catalan conjectures given Diophantine equation 128x + 961y =z2 gives a unique non-negative integer solution, that is (1, 1, 33). And the given Diophantine equation can be reduced in the form of 2x+31y=z2, where x, y and z are non-negative integer. Which gives the solution (7, 2, 18).

Catalan Conjectures, Diophantine Equation