Jacobi's four-square theorem

Jacobi's four-square theorem is an extension of Lagrange's four-square theorem, which states that every positive integer can be expressed as the sum of four squares. Jacobi's contribution to this area lies in his work on representing numbers as sums of squares and his formulation of a more explicit representation. The theorem states that the number of ways to represent a natural number \( n \) as a sum of four squares can be expressed through a specific counting function.