Among Lagrange's many achievements in number theory is a solution to the problem posed and solved by Fermat of finding a right triangle whose legs sum to a perfect square and whose hypotenuse is also a square. This article chronicles various appearances of the problem, including multiple solutions by Euler, all of which inadequately address completeness and minimality of solutions. Finally, we summarize and translate Lagrange's paper in which he solves the problem completely, thus successfully proving the minimality of Fermat's original solution.
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Goff, Christopher and Saclolo, Michael
"A History and Translation of Lagrange's "Sur quelques problèmes de l'analyse de Diophante'',"
Euleriana: 1(1), p. 62, Article 5.
Available at: https://scholarlycommons.pacific.edu/euleriana/vol1/iss1/5