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

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.


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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