J. Pure Appl. Algebra 212 (2008) (1) 271-274
### Sophie Frisch and Leonid Vaserstein

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.

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