- Title
- Quadratic form representations via generalized continuants
- Creator
- Delorme, Charles; Pineda-Villavicencio, Guillermo
- Date
- 2015
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/94811
- Identifier
- vital:10039
- Identifier
- ISSN:1530-7638
- Abstract
- 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. © 2015 University of Waterloo. All rights reserved.
- Publisher
- University of Waterloo
- Relation
- Journal of Integer Sequences Vol. 18, no. 6 (2015), p. Article number 15.6.4
- Rights
- © 2015 University of Waterloo
- Rights
- Open access
- Rights
- This metadata is freely available under a CCO license
- Subject
- Continuant; Fermats two-square theorem; Generalized continuant; Integer representation; 0101 Pure Mathematics; 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics
- Reviewed
- Hits: 1310
- Visitors: 1278
- Downloads: 0