Year: 2017
Type: article
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' theorem that every positive integer is representable as a sum of three triangular numbers.
DOI: 10.1112/blms.12068
Author: Eric T. Mortenson
Institution: Max Planck Institute for Mathematics
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2586890009