2017
Том 69
№ 9

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A Ring of Pythagorean Triples over Quadratic Fields

Harnchoowong A., Somboonkulavudi C.

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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.

English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 1, pp 153-159.

Citation Example: Harnchoowong A., Somboonkulavudi C. A Ring of Pythagorean Triples over Quadratic Fields // Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 135–139.

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