Explicit Formulas for Sums of Two and of Four Squares

Abstract

One of the oldest problems in number theory concerns the partition of an integer into a sum of squares. A famous result, first proved by Lagrange, is that any positive integer is a sum of four squares. In this chapter, we will not only prove this theorem, but also will find explicit formulas of Gauss and of Jacobi for the number of partitions of an integer into a sum of two and of four squares.