TY - JOUR
T1 - Polynomial parametrization of Pythagorean quadruples, quintuples and sextuples
AU - Frisch, Sophie
AU - Vaserstein, Leonid
PY - 2012/1
Y1 - 2012/1
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jpaa.2011.06.002
DO - 10.1016/j.jpaa.2011.06.002
M3 - Article
AN - SCOPUS:80052032234
SN - 0022-4049
VL - 216
SP - 184
EP - 191
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 1
ER -