Polynomial parametrization of pythagorean tuples

Leonid Vaserstein, Takis Sakkalis, Sophie Frisch

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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.

Original languageEnglish (US)
Pages (from-to)1261-1272
Number of pages12
JournalInternational Journal of Number Theory
Volume6
Issue number6
DOIs
Publication statusPublished - Sep 1 2010

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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