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ISRN Algebra
Volume 2012 (2012), Article ID 487275, 6 pages
http://dx.doi.org/10.5402/2012/487275
Research Article

On the Constructibility of Real 5th Roots of Rational Numbers with Marked Ruler and Compass

Mathematics Department, CALCampus, NH 03461, USA

Received 28 March 2012; Accepted 19 April 2012

Academic Editors: W. de Graaf and S. Raianu

Copyright © 2012 Elliot Benjamin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We demonstrate that there are infinitely many real numbers constructible by marked ruler and compass which are unique real roots of irreducible quintic polynomials over the field of rational numbers. This result can be viewed as a generalization of the historical open question of the constructibility by marked ruler and compass of real 5th roots of rational numbers. We obtain our results through marked ruler and compass constructions involving the intersection of conchoids and circles, and the application of number theoretic divisibility criteria.