New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square theorem

Abstract

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.

13 pages, 1 figure

References in corpus (1)

• A parametrization of equilateral triangles having integer coordinates