Joseph-Louis Lagrange four-square theorem quadratic forms Pell's equation Jayadeva
Joseph-Louis Lagrange (1736–1813) was the first to give full proofs of some of Fermat's and Euler's work and observations—for instance, the four-square theorem and the basic theory of the misnamed "Pell's equation" (for which an algorithmic solution was found by Fermat and his contemporaries, and also by Jayadeva and Bhaskara II before them.) He also studied quadratic forms in full generality (as opposed to 



m

X

2


+
n

Y

2




{\displaystyle mX^{2}+nY^{2}}

)—defining their equivalence relation, showing how to put them in reduced form, etc.
