New parametrization of A2+B2+C2=3D2A^2+B^2+C^2=3D^2 and Lagrange's four-square theorem

In this paper we provide a new parametrization for the diophantine equation $A^2+B^2+C^2=3D^2$ and give a series of corollaries. We discuss some connections with Lagrange's four-square theorem. As applications, we find new parameterizations of equilateral triangles and regular tetrahedrons having integer coordinates in three dimensions.Comment: 13 pages, 1 figur