Polynomial parametrization of pythagorean tuples

Leonid Vaserstein; Takis Sakkalis; Sophie Frisch

doi:10.1142/S1793042110003496

Polynomial parametrization of pythagorean tuples

Leonid Vaserstein
, Takis Sakkalis
, Sophie Frisch

Mathematics

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

2 Scopus citations

Abstract

A Pythagorean (k, l)-tuple over a commutative ring A is a vector x = (x_i) ∈ A^k+l, where k, l ∈ , k < l which satisfies σ_{i = 1}^k x_i² = σ_i= 1^l_k+i. In this paper, a polynomial parametrization of Pythagorean (k, l)-tuples over the ring F[t] is given, for l < 2. In the case where l = 1, solutions of the above equation are provided for k = 2, 3, 4, 5, and 9.

Original language	English (US)
Pages (from-to)	1261-1272
Number of pages	12
Journal	International Journal of Number Theory
Volume	6
Issue number	6
DOIs	https://doi.org/10.1142/S1793042110003496
State	Published - Sep 1 2010

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Access to Document

10.1142/S1793042110003496

Cite this

@article{6f619b39fe1342c293d676088c972b85,

title = "Polynomial parametrization of pythagorean tuples",

abstract = "A Pythagorean (k, l)-tuple over a commutative ring A is a vector x = (xi) ∈ Ak+l, where k, l ∈ , k < l which satisfies σi = 1k xi2 = σi= 1lk+i. In this paper, a polynomial parametrization of Pythagorean (k, l)-tuples over the ring F[t] is given, for l < 2. In the case where l = 1, solutions of the above equation are provided for k = 2, 3, 4, 5, and 9.",

author = "Leonid Vaserstein and Takis Sakkalis and Sophie Frisch",

year = "2010",

month = sep,

day = "1",

doi = "10.1142/S1793042110003496",

language = "English (US)",

volume = "6",

pages = "1261--1272",

journal = "International Journal of Number Theory",

issn = "1793-0421",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "6",

}

TY - JOUR

T1 - Polynomial parametrization of pythagorean tuples

AU - Vaserstein, Leonid

AU - Sakkalis, Takis

AU - Frisch, Sophie

PY - 2010/9/1

Y1 - 2010/9/1

N2 - A Pythagorean (k, l)-tuple over a commutative ring A is a vector x = (xi) ∈ Ak+l, where k, l ∈ , k < l which satisfies σi = 1k xi2 = σi= 1lk+i. In this paper, a polynomial parametrization of Pythagorean (k, l)-tuples over the ring F[t] is given, for l < 2. In the case where l = 1, solutions of the above equation are provided for k = 2, 3, 4, 5, and 9.

AB - A Pythagorean (k, l)-tuple over a commutative ring A is a vector x = (xi) ∈ Ak+l, where k, l ∈ , k < l which satisfies σi = 1k xi2 = σi= 1lk+i. In this paper, a polynomial parametrization of Pythagorean (k, l)-tuples over the ring F[t] is given, for l < 2. In the case where l = 1, solutions of the above equation are provided for k = 2, 3, 4, 5, and 9.

UR - https://www.scopus.com/pages/publications/77957550836

UR - https://www.scopus.com/pages/publications/77957550836#tab=citedBy

U2 - 10.1142/S1793042110003496

DO - 10.1142/S1793042110003496

M3 - Article

AN - SCOPUS:77957550836

SN - 1793-0421

VL - 6

SP - 1261

EP - 1272

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 6

ER -

Polynomial parametrization of pythagorean tuples

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this