Abstract: We give a parametrization of integer Pythagorean triples by a single triple of integer-valued polynomials in 4 variables and show that no single triple of polynomials with integer coefficients in any number of variables parametrizes all Pythagorean triples. Positive Pythagorean triples can be parametrized by a single triple of integer-valued polynomials, too. (Recall that an integer-valued polynomial is a polynomial with rational coefficients that gives an integer value whenever integers are substituted for the variables.)
2000 Mathematics Subject Classification: Primary 11D09; Secondary 11C08, 13F20.
PDF: S. Frisch, L. Vaserstein: Parametrization of Pythagorean triples by a single triple of polynomials