A Kronecker-type identity and the representations of a number as a sum of three squares

Abstract

By considering a limiting case of a Kronecker-type identity, we obtain an identity found by both Andrews and Crandall. We then use the Andrews-Crandall identity to give a new proof of a formula of Gauss for the representations of a number as a sum of three squares. From the Kronecker-type identity, we also deduce Gauss's theorem that every positive integer is representable as a sum of three triangular numbers.

EYPHKA! Theorem 1.6 and Section 4 are new

References in corpus (1)

• A double-sum Kronecker-type identity

Cited by in corpus (1)

• A new Andrews--Crandall-type identity and the number of integer solutions to $x^2+2y^2+2z^2=n$