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Searching for Diophantine quintuples

Cipu, Mihai; Trudgian, Tim

Description

We consider Diophantine quintuples {a,b,c,d,e}. These are sets of positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on current estimates to show that there are at most 5.441⋅10²⁶ Diophantine quintuples.

dc.contributor.authorCipu, Mihai
dc.contributor.authorTrudgian, Tim
dc.date.accessioned2016-08-24T05:17:30Z
dc.date.available2016-08-24T05:17:30Z
dc.identifier.issn0065-1036
dc.identifier.urihttp://hdl.handle.net/1885/107296
dc.description.abstractWe consider Diophantine quintuples {a,b,c,d,e}. These are sets of positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on current estimates to show that there are at most 5.441⋅10²⁶ Diophantine quintuples.
dc.publisherPolish Academy of Sciences, Institute of Mathematics
dc.rights© Instytut Matematyczny PAN, 2016. http://www.sherpa.ac.uk/romeo/issn/0065-1036/..."author can archive post-print (ie final draft post-refereeing)" from SHERPA/RoMEO site (as at 25/08/16).
dc.sourceActa Arithmetica
dc.subjectDiophantine m-tuples
dc.subjectPell equations
dc.subjectlinear forms in logarithms
dc.titleSearching for Diophantine quintuples
dc.typeJournal article
local.identifier.citationvolume173
dc.date.issued2016-05-18
local.publisher.urlhttps://www.impan.pl/
local.type.statusAccepted Version
local.contributor.affiliationTrudgian, T. S., Mathematical Sciences Institute, The Australian National University
local.bibliographicCitation.issue4
local.bibliographicCitation.startpage365
local.bibliographicCitation.lastpage382
local.identifier.doi10.4064/aa8254-2-2016
dcterms.accessRightsOpen Access
CollectionsANU Research Publications

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