PDF] New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square theorem
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Last updated 01 abril 2025
![PDF] New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square theorem](https://d3i71xaburhd42.cloudfront.net/40890436b6511a579be57c676d175ebbd8293125/1-Table1-1.png)
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.
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