Title: 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.