New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square theorem
Number Theory
2014-11-25 v1
Abstract
In this paper we provide a new parametrization for the diophantine equation 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.
Keywords
Cite
@article{arxiv.1411.6306,
title = {New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square theorem},
author = {Eugen J. Ionascu},
journal= {arXiv preprint arXiv:1411.6306},
year = {2014}
}
Comments
13 pages, 1 figure