Sums of Squares

Besides the theorems of Fermat and Lagrange on the representation of numbers as sums of two and four squares, there is also a proof of the Gauss–Legendre theorem on sums of three squares based on the use of Minkowski’s theorem on the existence of lattice points in a convex body. The tricky problems of finding representations of numbers as sums of squares, including Brillhart’s algorithm, are considered.