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Winter 2001 Algebraic Structures of Some Sets of Pythagorean Triples II
Marek Wójtowicz
Missouri J. Math. Sci. 13(1): 17-23 (Winter 2001). DOI: 10.35834/2001/1301017

Abstract

A natural bijection from $\mathbb{Z} ^2$ onto the set of all Pythagorean triples ${\mathcal P} = \{ (a,b,c) \in \mathbb{Z} ^3 : a^2 + b^2 = c^2 \}$ is given (Theorem 6). Consequently, all algebraic structures of $\mathbb{Z} ^2$ are carried in a natural way onto ${\mathcal P}$ (Theorems 7, 8, and 9). This solves the open problem of defining ring operations under which ${\mathcal P}$ is essentially a different ring than the one constructed by B. Dawson (Example, Section 5). This article and the enumeration of its sections and theorems is a continuation of the author's paper [3].

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Marek Wójtowicz. "Algebraic Structures of Some Sets of Pythagorean Triples II." Missouri J. Math. Sci. 13 (1) 17 - 23, Winter 2001. https://doi.org/10.35834/2001/1301017

Information

Published: Winter 2001
First available in Project Euclid: 5 October 2019

zbMATH: 1119.13301
MathSciNet: MR1816335
Digital Object Identifier: 10.35834/2001/1301017

Rights: Copyright © 2001 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.13 • No. 1 • Winter 2001
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