PDF] New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square theorem
Por um escritor misterioso
Last updated 11 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.
Molecular Dynamics Simulations Based on Newly Developed Force
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![PDF] New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square theorem](https://www.pnas.org/cms/asset/6b84d28e-1fa6-45bd-a831-0c1c79398f1e/keyimage.jpg)
Patterning of morphogenetic anisotropy fields
![PDF] New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square theorem](https://spj.science.org/cms/10.34133/2022/9868673/asset/49799e28-2e66-4cf9-9d16-19882d057fe6/assets/graphic/9868673.fig.001.jpg)
Molecular Computational Anatomy: Unifying the Particle to Tissue
![PDF] New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square theorem](https://www.pnas.org/cms/10.1073/pnas.2208027119/asset/61485b2c-8141-4699-a006-0bc8a2e99589/assets/images/large/pnas.2208027119fig03.jpg)
Quantitative prediction and measurement of Piezo's membrane
![PDF] New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square theorem](https://upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Plot_of_the_hypergeometric_function_2F1%28a%2Cb%3B_c%3B_z%29_with_a%3D2_and_b%3D3_and_c%3D4_in_the_complex_plane_from_-2-2i_to_2%2B2i_with_colors_created_with_Mathematica_13.1_function_ComplexPlot3D.svg/640px-thumbnail.svg.png)
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Frontiers Parameterization modeling for wind drift factor in oil
![PDF] New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square theorem](https://cyberleninka.org/viewer_images/535078/f/1.png)
On probability measures arising from lattice points on circles
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Optimal design and manufacture of variable stiffness laminated
![PDF] New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square theorem](https://upload.wikimedia.org/wikipedia/commons/thumb/9/96/Euclid%27s_algorithm_Book_VII_Proposition_2_3.svg/800px-Euclid%27s_algorithm_Book_VII_Proposition_2_3.svg.png)
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