Parametrization of Pythagorean triples by a single triple of polynomials. (English) Zbl 1215.11025

Frisch, Sophie; Vaserstein, Leonid

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.

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

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