Possible Solutions of the Diophantine equation x2+ky2=z2

Abstract

This paper is to identify the Diophantine equation x²+ky²=z² where k, x, y and z are integers satisfies; case 1: k=4m+2, has no integer solution if y  is odd, and have integer solutions (x, y, z) is where m is an integer, ab is a square number if y is even, case 2: k=2m+1 , have integer solutions (x, y, z) is   where m is an integer, ab is an odd square number if y is odd, and where m is an integer, ab is a square number if y is even, case 3: , k=4m have integer solutions (x, y, z) is  where m is an integer, ab is a square number,