Geodesic
Quadratic form representations via generalized continuants
Journal of integer sequences, Tome 18 (2015) no. 6
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.
Keywords: Fermat's two-square theorem, continuant, generalized continuant, integer representation 
@article{JIS_2015__18_6_a0,
     author = {Delorme,  Charles and Pineda-Villavicencio,  Guillermo},
     title = {Quadratic form representations via generalized continuants},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {6},
     zbl = {1378.11049},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_6_a0/}
}
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Delorme,  Charles; Pineda-Villavicencio,  Guillermo. Quadratic form representations via generalized continuants. Journal of integer sequences, Tome 18 (2015) no. 6. http://geodesic.mathdoc.fr/item/JIS_2015__18_6_a0/