Lagrange and the four-square theorem - Archive ouverte HAL
Por um escritor misterioso
Last updated 02 setembro 2024
In this article we will first provide an overview of Lagrange’s arithmetic work, written between 1768 and 1777. We then focus on the proof of the four-square theorem published in 1772, and shed light on the context of its implementation by relying on other memoirs by Lagrange and Leonhard Euler. By means of this analysis, our goal is to give a concrete vision of the arithmetic, algebraic and analytical methods and tools used by Lagrange in number theory and place his arithmetic practice in the context of the second half of the eighteenth century.
![Lagrange and the four-square theorem - Archive ouverte HAL](https://media.springernature.com/lw685/springer-static/image/art%3A10.1007%2Fs00200-022-00588-x/MediaObjects/200_2022_588_Figa_HTML.png)
Efficient computation of Riemann–Roch spaces for plane curves with ordinary singularities
Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares
![Lagrange and the four-square theorem - Archive ouverte HAL](https://journals.sagepub.com/cms/10.1177/1094342020953891/asset/images/large/10.1177_1094342020953891-fig6.jpeg)
Energy efficiency of nonlinear domain decomposition methods - Axel Klawonn, Martin Lanser, Oliver Rheinbach, Gerhard Wellein, Markus Wittmann, 2021
Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares
![Lagrange and the four-square theorem - Archive ouverte HAL](https://vonrohr.unige.ch/wp-content/uploads/2023/11/chemmat_vonrohr-750x450.jpg)
Publications - DQMP
![Lagrange and the four-square theorem - Archive ouverte HAL](https://0.academia-photos.com/attachment_thumbnails/74819809/mini_magick20211117-21063-18fbj3p.png?1637220633)
PDF) SAMPTA'09, International Conference on SAMPling Theory and Applications
![Lagrange and the four-square theorem - Archive ouverte HAL](https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-3-031-10141-0_13/MediaObjects/505458_1_En_13_Fig1_HTML.png)
Perspectives on Embedding the Historical Development of Mathematics in Mathematical Tasks
![Lagrange and the four-square theorem - Archive ouverte HAL](https://demonstrations.wolfram.com/RealDigitsCarpet/img/RealDigitsCarpet.png)
Lagrange's Four-Square Theorem Seen Using Polygons and Lines - Wolfram Demonstrations Project
Lagrange and the four-square theorem - Archive ouverte HAL
![Lagrange and the four-square theorem - Archive ouverte HAL](https://ars.els-cdn.com/content/image/1-s2.0-S0021999121007336-gr001.jpg)
Partial optimal transport for a constant-volume Lagrangian mesh with free boundaries - ScienceDirect
![Lagrange and the four-square theorem - Archive ouverte HAL](https://d3i71xaburhd42.cloudfront.net/38d75de91e3826a1b51c77a96c4410be37e8ccdb/28-Figure3-1.png)
PDF] Analytical Parameterization of Rotors and Proof of a Goldberg Conjecture by Optimal Control Theory
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