On the Diophantine Equation $2^x + 17^y =Z^2$

Abstract

We show that the Diophantine equation 2x+ 17y = z^2, has exactlyve solutions (x; y; z) in positive integers. The only solutions are (3; 1; 5), (5; 1; 7),(6; 1; 9), (7; 3; 71) and (9; 1; 23). This note, in turn, addresses an open problemproposed by Sroysang in [10].DOI : http://dx.doi.org/10.22342/jims.22.2.422.177-18