Vaserstein, Leonid; Sakkalis, Takis; Frisch, Sophie Polynomial parametrization of Pythagorean tuples. (English) Zbl 1237.11015 Int. J. Number Theory 6, No. 6, 1261-1272 (2010). A Pythagorean \((k,l)\)-tuple over a commutative ring \(A\) is a vector \((x_1,\dots,x_{k+l}) \in A^{k+l}\) such that \(x_1^2 + \dots + x_k^2 = x_{k+1}^2 + \dots + x_{k+l}^2\). In the present paper, the authors give a polynomial parametrization of Pythagorean \((k,l)\)-tuples over the ring \(F[t]\) (where \(F\) is a field), for \(l\geq 2\). They also give the solutions for the cases \(l=1\) and \(k=2,3,4,5,9\). Reviewer: Andrej Dujella (Zagreb) Cited in 2 Documents MSC: 11D09 Quadratic and bilinear Diophantine equations 11E12 Quadratic forms over global rings and fields 11E25 Sums of squares and representations by other particular quadratic forms Keywords:Pythagorean tuples; polynomial parametrization; fields; polynomial rings; orthogonal transformations PDFBibTeX XMLCite \textit{L. Vaserstein} et al., Int. J. Number Theory 6, No. 6, 1261--1272 (2010; Zbl 1237.11015) Full Text: DOI References: [1] Carmichael R. D., Diofantine Analysis (1915) [2] Cass D., Proc. Amer. Math. Soc. 109 pp 1– [3] DOI: 10.1016/j.jpaa.2007.05.019 · Zbl 1215.11025 [4] Geramita A. V., Lecture Notes in Pure and Applied Mathematics 43, in: Orthogonal Designs: Quadratic Forms and Hadamard Matrices (1979) · Zbl 0411.05023 [5] DOI: 10.1016/S0022-314X(03)00015-5 · Zbl 1026.11058 [6] DOI: 10.1016/j.cam.2008.09.022 · Zbl 1166.53002 [7] Vaserstein L. N., Izv. Akad. Nauk. Ser. Mat. 40 pp 993– This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.