Quadratic Form Representations via Generalized Continuants
Laboratoire de Recherche en Informatique
Université Paris Sud
91405 Orsay Cedex
Centre for Informatics and Applied Optimisation
Federation University Australia
Mount Helen, Victoria 3350
H. J. S. Smith proved Fermat's two-square theorem using the notion of
palindromic continuants. In this paper we extend Smith's approach to
proper binary quadratic form representations in some commutative
Euclidean rings, including rings of integers and rings of polynomials
over fields of odd characteristic. Also, we present new deterministic
algorithms for finding the corresponding proper representations.
Full version: pdf,
(Concerned with sequences
Received July 18 2014; revised version received April 21 2015; May 27 2015.
Published in Journal of Integer Sequences, June 1 2015.
Journal of Integer Sequences home page