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Spring 1994 A Ring of Pythagorean Triples
Bryan Dawson
Missouri J. Math. Sci. 6(2): 72-77 (Spring 1994). DOI: 10.35834/1994/0602072

Abstract

A one-to-one correspondence between the set of all Pythagorean triples and ${\mathbb Z} \times {\mathbb Z}$ is established, resulting in a ring of Pythagorean triples.

A triple $\langle a,b,c \rangle$ is called a Pythagorean triple if $a, b, {\text {and }} c$ are integers such that $a^2+b^2=c^2$. It seems natural to ask whether operations can be defined on the set $P$ of all Pythagorean triples in such a way as to give $P$ a ring structure. In fact, since a Pythagorean triple is determined by any two of the three integers, one might attempt to obtain a ring structure isomorphic to ${\mathbb Z} \times {\mathbb Z}$ (where ${\mathbb Z}$ represents the set of integers and the operations on ${\mathbb Z} \times {\mathbb Z}$ are defined coordinatewise) by finding a one-to-one correspondence between $P$ and ${\mathbb Z} \times {\mathbb Z}$. The establishment of such a correspondence and the resulting ring structure is the objective of this paper.

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Bryan Dawson. "A Ring of Pythagorean Triples." Missouri J. Math. Sci. 6 (2) 72 - 77, Spring 1994. https://doi.org/10.35834/1994/0602072

Information

Published: Spring 1994
First available in Project Euclid: 17 December 2019

zbMATH: 1097.11527
MathSciNet: MR1322441
Digital Object Identifier: 10.35834/1994/0602072

Rights: Copyright © 1994 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.6 • No. 2 • Spring 1994
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