Article ID Journal Published Year Pages File Type
6415572 Journal of Number Theory 2013 19 Pages PDF
Abstract

Kaplansky [2003] proved a theorem on the simultaneous representation of a prime p by two different principal binary quadratic forms. Later, Brink found five more like theorems and claimed that there were no others. By putting Kaplansky-like theorems into the context of threefield identities after Andrews, Dyson, and Hickerson, we find that there are at least two similar results not on Brinkʼs list. We also show how such theorems are related to results of Muskat on binary quadratic forms.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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