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Polynomial parametrization of Pythagorean quadruples, quintuples and sextuples. (English) Zbl 1273.11053
Summary: For $n=4$ or 6, the Pythagorean $n$-tuples admit a parametrization by a single $n$-tuple of polynomials with integer coefficients (which is impossible for $n=3$). For $n=5$, there is an integer-valued polynomial Pythagorean 5-tuple which parametrizes Pythagorean 5-tuples (similar to the case $n=3$). Pythagorean quadruples are closely related to (integer) Descartes quadruples, which we also parametrize by a Descartes quadruple of polynomials with integer coefficients.
MSC:
11D09Quadratic and bilinear diophantine equations
11D72Equations in many variables
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