All the Solutions of the Diophantine Equation $p^4 + q^2 = z^2$ when p is Prime

In this paper, we consider the title equation in the particular case when p is prime.It is established that the equation has exactly two distinct solutions.One solution for each and every prime p ≥ 3, the other solution for each and every prime p ≥ 2. The solutions are demonstrated for each prime p in the form of identities.Furthermore, the connection between the equation and the Pythagorean triples is also discussed when the prime p is replaced by any odd value A ≥ 3.