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arXiv · 1702.01627

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

Eric T. Mortenson
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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.

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Eric T. Mortenson. 2017-02-06. A Kronecker-type identity and the representations of a number as a sum of three squares. https://doi.org/10.1112/blms.12068

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