OPEN PROBLEM
It is to be noted that all finding of the solutions of Diophantine equation in the case of
2^x+p^y=z^2 where p is prime in general is still an open problem. For example, it is not known
how to find all non-negative integer solutions of 2^x+p^y=z^2 where p = 7, 13, 29, 37 or 257.