Journal of Integer Sequences, Vol. 18 (2015), Article 15.6.4

Quadratic Form Representations via Generalized Continuants

Charles Delorme
Laboratoire de Recherche en Informatique
Bâtiment 650
Université Paris Sud
91405 Orsay Cedex

Guillermo Pineda-Villavicencio
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.

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(Concerned with sequences A003655 and A014602.)

Received July 18 2014; revised version received April 21 2015; May 27 2015. Published in Journal of Integer Sequences, June 1 2015.

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