What is the Value of Taxicab(6)? An Update

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dc.contributor.author Calude, C.S en
dc.contributor.author Calude, E en
dc.contributor.author Dinneen, Michael en
dc.date.accessioned 2009-04-16T23:09:54Z en
dc.date.available 2009-04-16T23:09:54Z en
dc.date.issued 2005-04 en
dc.identifier.citation CDMTCS Research Reports CDMTCS-261 (2005) en
dc.identifier.issn 1178-3540 en
dc.identifier.uri http://hdl.handle.net/2292/3768 en
dc.description.abstract The famous story of the number 1729, the smallest integer which can be expressed as the sum of two positive cubes in two different ways, motivated the introduction of Taxicab Numbers. The smallest number expressible as the sum of two cubes in n different ways is called Taxicab(n). So, Taxicab(2) = 1729. Further on, Taxicab(5) = 48988659276962496. Computing Taxicab(n) is challenging and interesting, both from mathematical and programming points of view. The exact value of Taxicab(6) is not known; in view of the results obtained by Bernstein [1] and Rathbun [14] it follows that Taxicab(6) is in the interval [10¹⁸, 24153319581254312065344]. In [5] we proved that with probability greater than 99%, Taxicab(6) = 24153319581254312065344. In this note we improve the method used in [5] in two ways: we use (1) a larger, and (2) a better quality random sampling, namely, a sample of 562,500 quantum random integers drawn from the above mentioned interval using Quantis, [10]. As a result, we prove that the above value for Taxicab(6) is true with probability greater than 99.8%. en
dc.publisher Department of Computer Science, The University of Auckland, New Zealand en
dc.relation.ispartofseries CDMTCS Research Report Series en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.source.uri http://www.cs.auckland.ac.nz/staff-cgi-bin/mjd/secondcgi.pl?serial en
dc.title What is the Value of Taxicab(6)? An Update en
dc.type Technical Report en
dc.subject.marsden Fields of Research::280000 Information, Computing and Communication Sciences en
dc.rights.holder The author(s) en
dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en


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