Parametrization of Pythagorean triples by a single triple of polynomials

Sophie Frisch; Leonid Vaserstein

doi:10.1016/j.jpaa.2007.05.019

Parametrization of Pythagorean triples by a single triple of polynomials

Sophie Frisch, Leonid Vaserstein

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

It is well known that Pythagorean triples can be parametrized by two triples of polynomials with integer coefficients. We show that no single triple of polynomials with integer coefficients in any number of variables is sufficient, but that there exists a parametrization of Pythagorean triples by a single triple of integer-valued polynomials.

Original language	English (US)
Pages (from-to)	271-274
Number of pages	4
Journal	Journal of Pure and Applied Algebra
Volume	212
Issue number	1
DOIs	https://doi.org/10.1016/j.jpaa.2007.05.019
State	Published - Jan 2008

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jpaa.2007.05.019

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title = "Parametrization of Pythagorean triples by a single triple of polynomials",

abstract = "It is well known that Pythagorean triples can be parametrized by two triples of polynomials with integer coefficients. We show that no single triple of polynomials with integer coefficients in any number of variables is sufficient, but that there exists a parametrization of Pythagorean triples by a single triple of integer-valued polynomials.",

author = "Sophie Frisch and Leonid Vaserstein",

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doi = "10.1016/j.jpaa.2007.05.019",

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AU - Vaserstein, Leonid

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AB - It is well known that Pythagorean triples can be parametrized by two triples of polynomials with integer coefficients. We show that no single triple of polynomials with integer coefficients in any number of variables is sufficient, but that there exists a parametrization of Pythagorean triples by a single triple of integer-valued polynomials.

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DO - 10.1016/j.jpaa.2007.05.019

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AN - SCOPUS:34548394147

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VL - 212

SP - 271

EP - 274

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 1

ER -

Parametrization of Pythagorean triples by a single triple of polynomials

Abstract

All Science Journal Classification (ASJC) codes

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