Searching for Diophantine quintuples
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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.author | Cipu, Mihai | |
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dc.contributor.author | Trudgian, Tim | |
dc.date.accessioned | 2016-08-24T05:17:30Z | |
dc.date.available | 2016-08-24T05:17:30Z | |
dc.identifier.issn | 0065-1036 | |
dc.identifier.uri | http://hdl.handle.net/1885/107296 | |
dc.description.abstract | 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.publisher | Polish 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.source | Acta Arithmetica | |
dc.subject | Diophantine m-tuples | |
dc.subject | Pell equations | |
dc.subject | linear forms in logarithms | |
dc.title | Searching for Diophantine quintuples | |
dc.type | Journal article | |
local.identifier.citationvolume | 173 | |
dc.date.issued | 2016-05-18 | |
local.publisher.url | https://www.impan.pl/ | |
local.type.status | Accepted Version | |
local.contributor.affiliation | Trudgian, T. S., Mathematical Sciences Institute, The Australian National University | |
local.bibliographicCitation.issue | 4 | |
local.bibliographicCitation.startpage | 365 | |
local.bibliographicCitation.lastpage | 382 | |
local.identifier.doi | 10.4064/aa8254-2-2016 | |
dcterms.accessRights | Open Access | |
Collections | ANU Research Publications |
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