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Ukrainian Mathematical Journal

, Volume 66, Issue 1, pp 153–159 | Cite as

A Ring of Pythagorean Triples over Quadratic Fields

  • C. Somboonkulavudi
  • A. Harnchoowong
Article
  • 78 Downloads

Let K be a quadratic field and let R be the ring of integers of K such that R is a unique factorization domain. The set P of all Pythagorean triples in R is partitioned into P η , sets of triples 〈αβγ〉 in P where η = γ − β. We show the ring structures of each P η and P from the ring structure of R.

Keywords

Ring Structure Commutative Ring Integer Number Mathematical Journal Previous Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    B. Dawson, “A ring of Pythagorean triples,” Missouri J. Math. Sci., 6, 72–77 (1994).zbMATHMathSciNetGoogle Scholar
  2. 2.
    J. T. Cross, “Primitive Pythagorean triples of Gaussian integers,” Math. Mag., 59, No. 2, 106–110 (1986).CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • C. Somboonkulavudi
    • 1
  • A. Harnchoowong
    • 1
  1. 1.Chulalongkorn UniversityBangkokThailand

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