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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 66, Issue 3


On the congruent number problem over integers of cyclic number fields

Albertas Zinevičius
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  • Department of Mathematics and Informatics Vilnius University Naugarduko 24 LT-03225 Vilnius LITHUANIA
  • Institute of Mathematics and Informatics Akademijos 4 LT-08663 Vilnius LITHUANIA
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Published Online: 2016-08-17 | DOI: https://doi.org/10.1515/ms-2015-0158


Given a cyclic field extension K/ℚ of degree d and a nonzero rational integer m, we show that the equation mp2 = x4 - y2 has no nontrivial solutions in K/Q when p belongs to a subset of rational prime numbers of relative density at least φ(d)/(2d).

MSC 2010: Primary 11D45; 11H06

keywords: congruent numbers; cyclic extensions; rings of integers; prime numbers


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About the article

Received: 2013-01-16

Accepted: 2014-01-08

Published Online: 2016-08-17

Published in Print: 2016-06-01

Citation Information: Mathematica Slovaca, Volume 66, Issue 3, Pages 561–564, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0158.

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