Ukrainian Mathematical Journal

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

A Ring of Pythagorean Triples over Quadratic Fields

  • C. Somboonkulavudi
  • A. Harnchoowong

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.


Ring Structure Commutative Ring Integer Number Mathematical Journal Previous Theorem 
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  1. 1.
    B. Dawson, “A ring of Pythagorean triples,” Missouri J. Math. Sci., 6, 72–77 (1994).zbMATHMathSciNetGoogle Scholar
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    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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