On the Diophantine Equation 22nx - py = z2, where p is a prime

In this paper, we study the Diophantine equation 2(2nx) - p(y) = z(2), where n is a positive integer and p is a prime number. For p = 2, we find the set of all solutions in non-negative integers x, y and z given by {(x, y, z)} = {(0, 0, 0)} boolean OR {(t, 2nt, 0)}. For p an odd prime number, we find the set of all solutions in non-negative integers x, y and z given by {(x, y, z)} = {(0, 0, 0)} boolean OR {(q-1/n, 1, 2(q-1) - 1)} for prime p = 2(q)1, where q is also a prime number. For p equivalent to 3(mod4) not of the form 2(q)1, we only have the trivial solution (x, y, z) = (0,0, 0).