PDF] New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square theorem
Por um escritor misterioso
Last updated 25 março 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.
Example 2: relative error of FEM solution for the potential field
![PDF] New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square theorem](https://www.mdpi.com/files/uploaded/covers/mathematics/big_cover-mathematics-v10-i10.png)
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Reduced order modeling of parametrized systems through
![PDF] New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square theorem](https://www.mdpi.com/mathematics/mathematics-10-04395/article_deploy/html/images/mathematics-10-04395-g001.png)
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![PDF] New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square theorem](https://pubs.acs.org/cms/10.1021/acs.jctc.2c00460/asset/images/medium/ct2c00460_0012.gif)
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