Frisch, Sophie; Vaserstein, Leonid Parametrization of Pythagorean triples by a single triple of polynomials. (English) Zbl 1215.11025 J. Pure Appl. Algebra 212, No. 1, 271-274 (2008). Summary: It is well known that Pythagorean triples can be parametrized by two triples of polynomials with integer coefficients. We show that no single triple of polynomials with integer coefficients in any number of variables is sufficient, but that there exists a parametrization of Pythagorean triples by a single triple of integer-valued polynomials. Cited in 8 Documents MSC: 11D09 Quadratic and bilinear Diophantine equations 11D85 Representation problems 11C08 Polynomials in number theory 13F20 Polynomial rings and ideals; rings of integer-valued polynomials × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] D.F. Anderson, P.-J. Cahen, S. Chapman, W.W. Smith, Some factorization properties of the ring of integer-valued polynomials, in: Anderson and Dobbs [2], pp. 125-142; D.F. Anderson, P.-J. Cahen, S. Chapman, W.W. Smith, Some factorization properties of the ring of integer-valued polynomials, in: Anderson and Dobbs [2], pp. 125-142 · Zbl 0883.13018 [2] (Anderson, D. F.; Dobbs, D., Zero-Dimensional Commutative Rings (Knoxville, TN, 1994). Zero-Dimensional Commutative Rings (Knoxville, TN, 1994), Lecture Notes in Pure and Applied Mathematics, vol. 171 (1995), Dekker) · Zbl 0872.00033 [3] Cahen, P.-J.; Chabert, J.-L., Elasticity for integral-valued polynomials, J. Pure Appl. Algebra, 103, 303-311 (1995) · Zbl 0843.12001 [4] Cahen, P.-J.; Chabert, J.-L., (Integer-Valued Polynomials. Integer-Valued Polynomials, Mathematical Surveys and Monographs, vol. 48 (1997), Amer. Math. Soc.) · Zbl 0884.13010 [5] Chapman, S.; McClain, B. A., Irreducible polynomials and full elasticity in rings of integer-valued polynomials, J. Algebra, 293, 595-610 (2005) · Zbl 1082.13001 [6] S. Frisch, Remarks on polynomial parametrization of sets of integer points, Comm. Algebra. (in press); S. Frisch, Remarks on polynomial parametrization of sets of integer points, Comm. Algebra. (in press) · Zbl 1209.11038 [7] Hlawka, E.; Schoißengeier, J., Zahlentheorie. Eine Einführung (1979), Manz: Manz Vienna · Zbl 0412.10001 [8] L. Vaserstein, Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups, Ann. Math. (in press); L. Vaserstein, Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups, Ann. Math. (in press) · Zbl 1221.11082 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.