Introduction

The following theorem is relating to the Théorie of the numbers.

One poses $r\_4\; (N)$ as being the number of way of breaking up the whole $n$ in the form of a sum of 4 square.

The theorem of Jacobi is the statement of the following result:

$\backslash \; forall\; N\; \backslash \; in\; \backslash \; mathbb\; \{NR\}\; ^*,\; r\_4\; (N)\; =\; 8\; \backslash \; sum\_\; \{D|N,\; D\; \backslash \; not\; \backslash \; equiv\; 0\}\; \{D\}$

It is noticed that the Théorème of the four squares of Lagrange is a consequence of this one.