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Article: Fermat's polygonal number theorem for repeated generalized polygonal numbers

TitleFermat's polygonal number theorem for repeated generalized polygonal numbers
Authors
Banerjee, SBatavia, MSKane, BRKyranbay, MPark, DSaha, SSo, HCVaryani, PY
Issue Date2020
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnt
Citation
Journal of Number Theory (Forthcoming) How to Cite?
AbstractIn this paper, we consider sums of generalized polygonal numbers with repeats, generalizing Fermat's polygonal number theorem which was proven by Cauchy. In particular, we obtain the minimal number of generalized m-gonal numbers required to represent every positive integer and we furthermore generalize this result to obtain optimal bounds when many of the generalized m-gonal numbers are repeated r times, where r is a fixed positive integer.
Persistent Identifierhttp://hdl.handle.net/10722/284071
ISSN
0022-314X
2021 Impact Factor: 0.679
2020 SCImago Journal Rankings: 0.634

 

DC FieldValueLanguage
dc.contributor.authorBanerjee, S-
dc.contributor.authorBatavia, MS-
dc.contributor.authorKane, BR-
dc.contributor.authorKyranbay, M-
dc.contributor.authorPark, D-
dc.contributor.authorSaha, S-
dc.contributor.authorSo, HC-
dc.contributor.authorVaryani, PY-
dc.date.accessioned2020-07-20T05:55:52Z-
dc.date.available2020-07-20T05:55:52Z-
dc.date.issued2020-
dc.identifier.citationJournal of Number Theory (Forthcoming)-
dc.identifier.issn0022-314X-
dc.identifier.urihttp://hdl.handle.net/10722/284071-
dc.description.abstractIn this paper, we consider sums of generalized polygonal numbers with repeats, generalizing Fermat's polygonal number theorem which was proven by Cauchy. In particular, we obtain the minimal number of generalized m-gonal numbers required to represent every positive integer and we furthermore generalize this result to obtain optimal bounds when many of the generalized m-gonal numbers are repeated r times, where r is a fixed positive integer.-
dc.languageeng-
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnt-
dc.relation.ispartofJournal of Number Theory-
dc.titleFermat's polygonal number theorem for repeated generalized polygonal numbers-
dc.typeArticle-
dc.identifier.emailBanerjee, S: zsoumya@hku.hk-
dc.identifier.emailKane, BR: bkane@hku.hk-
dc.identifier.emailPark, D: pdy1016@HKUCC-COM.hku.hk-
dc.identifier.authorityKane, BR=rp01820-
dc.identifier.hkuros310824-
dc.publisher.placeUnited States-
dc.identifier.issnl0022-314X-

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