## Diophantine equations : 2^A – 3^B = 3^D – 2^C

Find all the solutions to the Diophantine equations

$2^{A} \; - \; 3^{B} \; = \; 3^{D} \; - \; 2^{C}$
$2^{A} \; - \; 3^{B} \; = \; 2^{C} \; + \; 3^{D}$
$3^{B} \; - \; 2^{A} \; = \; 2^{C} \; + \; 3^{D}$