Solutions of the Diophantine Equation X2+py2=z2

Abstract

This paper is to identify the Diophantine equation   where   is a prime number and   and   are integers satisfies; case 1:  , has no integer solution if   is odd, and have integer solutions   is   where   is a square number if   is even, case 2:  , have integer solutions   is  where   is an odd square number if   is odd, and    where   is a square number if   is even.