ON THE EXPONENTIAL DIOPHANTINE EQUATION
ON THE EXPONENTIAL DIOPHANTINE EQUATION
Abstract Let $m$ , $a$ , $c$ be positive integers with $a\equiv 3, 5~({\rm mod} \hspace{0.334em} 8)$ . We show that when $1+ c= {a}^{2} $ , the exponential Diophantine equation $\mathop{({m}^{2} + 1)}\nolimits ^{x} + \mathop{(c{m}^{2} - 1)}\nolimits ^{y} = \mathop{(am)}\nolimits ^{z} $ has only the positive integer solution …