ON THE DIOPHANTINE EQUATION x2 = y2 + 3z2

Abstract

In an earlier paper, the solutions of the Diophantine equations a2 = b2 + c2  bc, which arise in connection with the 60-degree and 120-degree S-related and Z-related triangles, were studied to some extent. This paper considers the Diophantine equation x2 = y2 + 3z2, which unravels some new facts about the solutions of the Diophantine equations a2 = b2 + c2  bc.