Polynomial parametrization of Pythagorean quadruples, quintuples and sextuples

Sophie Frisch, Leonid Vaserstein

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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
Volume216
Issue number1
DOIs
StatePublished - Jan 1 2012

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Quadruple
Parametrization
René Descartes
Polynomial
Integer
Integer-valued Polynomials
n-tuple
Coefficient

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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Polynomial parametrization of Pythagorean quadruples, quintuples and sextuples. / Frisch, Sophie; Vaserstein, Leonid.

In: Journal of Pure and Applied Algebra, Vol. 216, No. 1, 01.01.2012, p. 184-191.

Research output: Contribution to journalArticle

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