Polynomial parametrization of Pythagorean quadruples, quintuples and sextuples

Sophie Frisch, Leonid Vaserstein

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)184-191
Number of pages8
JournalJournal of Pure and Applied Algebra
Issue number1
StatePublished - Jan 2012

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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