A Ring of Pythagorean Triples over Quadratic Fields

  • A. Harnchoowong
  • C. Somboonkulavudi

Abstract

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.
Published
25.01.2014
How to Cite
HarnchoowongA., and SomboonkulavudiC. “A Ring of Pythagorean Triples over Quadratic Fields”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 1, Jan. 2014, pp. 135–139, http://umj.imath.kiev.ua/index.php/umj/article/view/2117.
Section
Short communications