Lagrange and the four-square theorem - Archive ouverte HAL

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.

Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares

Lagrange's Four-Square Theorem Seen Using Polygons and Lines - Wolfram Demonstrations Project

Lagrange's Four-Square Theorem Seen Using Polygons and Lines - Wolfram Demonstrations Project

Publications - DQMP

A non-overlapping domain decomposition method with perfectly matched layer transmission conditions for the Helmholtz equation - ScienceDirect

Energy efficiency of nonlinear domain decomposition methods - Axel Klawonn, Martin Lanser, Oliver Rheinbach, Gerhard Wellein, Markus Wittmann, 2021

What is lagrange theorem? - Quora

Lagrange's Four-Square Theorem -- from Wolfram MathWorld

Thesis Bourget Antoine, PDF, Boson

Partial optimal transport for a constant-volume Lagrangian mesh with free boundaries - ScienceDirect

Energy efficiency of nonlinear domain decomposition methods - Axel Klawonn, Martin Lanser, Oliver Rheinbach, Gerhard Wellein, Markus Wittmann, 2021

Energy efficiency of nonlinear domain decomposition methods - Axel Klawonn, Martin Lanser, Oliver Rheinbach, Gerhard Wellein, Markus Wittmann, 2021