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Article: Representing sets with sums of triangular numbers

TitleRepresenting sets with sums of triangular numbers
Authors
Issue Date2009
Citation
International Mathematics Research Notices, 2009, v. 2009 n. 17, p. 3264-3285 How to Cite?
AbstractWe investigate here sums of triangular numbers f (x) := ∑ i b iT xi where T n is the nth triangular number. We show that for a set of positive integers S, there is a finite subset S 0 such that f represents S if and only if f represents S 0. However, computationally determining S 0 is ineffective for many choices of S. We give an explicit and efficient algorithm to determine the set S 0 under certain generalized Riemann hypotheses, and implement the algorithm to determine S 0 when S is the set of all odd integers. © The Author 2009. Published by Oxford University Press. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/192198
ISSN
2015 Impact Factor: 1.031
2015 SCImago Journal Rankings: 2.052
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorKane, Ben_US
dc.date.accessioned2013-10-23T09:27:18Z-
dc.date.available2013-10-23T09:27:18Z-
dc.date.issued2009en_US
dc.identifier.citationInternational Mathematics Research Notices, 2009, v. 2009 n. 17, p. 3264-3285en_US
dc.identifier.issn1073-7928en_US
dc.identifier.urihttp://hdl.handle.net/10722/192198-
dc.description.abstractWe investigate here sums of triangular numbers f (x) := ∑ i b iT xi where T n is the nth triangular number. We show that for a set of positive integers S, there is a finite subset S 0 such that f represents S if and only if f represents S 0. However, computationally determining S 0 is ineffective for many choices of S. We give an explicit and efficient algorithm to determine the set S 0 under certain generalized Riemann hypotheses, and implement the algorithm to determine S 0 when S is the set of all odd integers. © The Author 2009. Published by Oxford University Press. All rights reserved.-
dc.languageengen_US
dc.relation.ispartofInternational Mathematics Research Noticesen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleRepresenting sets with sums of triangular numbersen_US
dc.typeArticleen_US
dc.description.naturepostprint-
dc.identifier.doi10.1093/imrn/rnp053en_US
dc.identifier.scopuseid_2-s2.0-80052878924en_US
dc.identifier.volume2009en_US
dc.identifier.issue17en_US
dc.identifier.spage3264en_US
dc.identifier.epage3285en_US
dc.identifier.isiWOS:000269205300006-

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