Abstract:
We first show the condition for which the Diophantine equation w^x+(w-1)^y=z^2, where w is a positive integer of the form 24N+5, may admit nonnegative integer solutions. Then, using this condition and the modular arithmetic method, we demonstrate that the Diophantine equation 29^x+28^y=z^2 has no solution in nonnegative integers.