descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Conference object 01 Jan 2019Embargo end date: 01 Jan 2017 English Publisher:Elsevier BVJournal:Journal of Number Theory, volume 194, pages 170-217 (issn: 0022-314X,

Authors: Marija Bliznac Trebješanin; Alan Filipin;

doi: 10.1016/j.jnt.2018.07.013 , 10.48550/arxiv.1704.01874

arXiv: http://arxiv.org/abs/1704.01874

Nonexistence of D(4)-quintuples

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Abstract

In this paper we prove a conjecture that $D(4)$-quintuple does not exist using both classical and new methods. Also, we give a new version of the Rickert's theorem that can be applied on some $D(4)$-quadruples.

38 pages; some mistakes corrected, some explanations added

Related Organizations

University of Zagreb
Croatia
University of Split
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University of Zagreb, Faculty of Science
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SVEUCILISTE U ZAGREBU FAKULTET ELEKTROTEHNIKE I RACUNARSTVA
Croatia

Keywords

Pell equations, Mathematics - Number Theory, Reduction method, FOS: Mathematics, Number Theory (math.NT), Diophantine m-tuples ; Pell equations ; Reduction method, Diophantine m-tuples

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