Title
New parametrization of A2 + B2 + C2 = 3D2 and langrange’s four-square theorem
Document Type
Article
Publication Date
1-1-2016
Publication Title
Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica
Volume
3
First Page
823
Last Page
833
Keywords
Eisenstein integers, Equilateral triangles, Lagrange’s four square theorem, Quadratic forms, Quaternion integers, System of diophantine equation
Abstract
© 2016, Universitatii Al.I.Cuza din Iasi. All rights reserved. In this paper we provide a new parametrization for the diophantine equation A2 +B2 +C2 = 3D2 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.
Recommended Citation
Ionascu, Eugen J., "New parametrization of A2 + B2 + C2 = 3D2 and langrange’s four-square theorem" (2016). Faculty Bibliography. 3012.
https://csuepress.columbusstate.edu/bibliography_faculty/3012
