English

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 A2+B2+C2=3D2A^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.

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