Sums of three squares

Abstract

We make use of an elegant method of Professor H. Davenport [l] in the Geometry of Numbers. Without loss of generality we will prove Theorem 1 only when m is square free. (In the following m will be assumed to be square free.) In §1 we shall prove Theorem 1 when m = 3 (mod 8). In §2 we will merely outline the proof when m = l, 2, 5, 6 (mod 8), as the proof is almost identical except for minor changes. We shall only assume the reader is familiar with the elementary facts of the law of quadratic reciprocity, Minkowski's Theorem on lattice points contained within convex symmetric bodies; and when a positive integer is the sum of two squares.

Locations

• Proceedings of the American Mathematical Society - View - PDF