mycoreobjectrosdok_document_0000027962rosdok_document_0000027962rosdokdocumentrosdok_derivate_00002298922026-10-13T14:58:35.723Z2026-10-13T14:35:02.872ZMCRJANITOReditorKEpublished1rosdok_derivate_0000229892truetruederivate_types:fulltextVolltextfulltextwf_edit_epub wf_register_epubstate:publishedstate:publishedveröffentlichtpublishedrosdok_id000058261986691772Oau2026-10-132026-10-13T14:56:01ZrdaConverted from PICA to MODS using Pica2MODS XSLT Transformer 2.14-SNAPSHOT [SCM: "" "" ""] with mode 'DEFAULT'.WorkingpaperAproof of the theorem according to which every prime number possesses property BIn the present thesis, we prove a conjecture belonging to a subbranch of additive combinatorics that is called combinatorial zero-sum theory. Denoting by p an arbitrary prime number, it has been known for about forty years that every sequence (P1, P2,..., P2p-1) consisting of 2p-1points from the affine plane Fp^2 possesses a non-empty subsequence the sum of whose elements equals zero. This fact has been first shown independently by Kruyswijk and Olson and is nowadays known to be an easy consequence of Alon´s combinatorial Nullstellensatz. A less obvious question asksfor a classification of all those sequences (P1, P2,..., P2p-2) of lenght 2p-2 whose only zero-sum subsequence is the empty one. This problem has been investigated by several researchers and in this respect a certain conjecture implying in particular that any such sequence contains p-2 equal points has attracted a great deal of attention in recent years. A precise version of this conjecture will be given below. By definition, the prime number p has property B if and only if it behaevs in accordance with the conjecture under discussion; by developing for the first time a powerful method for tackling such inverse problems over Fp^2, we prove the result alluded to in the title.ChristianReiherVerfasserInauthttps://purl.uni-rostock.de/rosdok/id00005826urn:nbn:de:gbv:28-rosdok_id00005826-510.18453/rosdok_id00005826510 MathematikMathematisch-Naturwissenschaftliche Fakultätalle Rechte vorbehaltenRechteinhaber Universität Rostockfrei zugänglich (Open Access)Lizenz Metadaten: CC0en1 Online-Ressource (29 Seiten)2010University of Rostock, Institute of MathematicsRostockmonographic20102026Universitätsbibliothek RostockRostock2026Universitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00005826Christian Reiherrosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-810/10010-0001doctype:epubdoctype:epubDokumenttypDocument typedoctype:epub.workingpaperdoctype:epub.workingpaperWorkingpaperworking paperdiniPublType:workingPaper diniPublType2022:WorkingPaperinfo:eu-repo/semantics/workingPaperdocumentdiniPublType2022:WorkingPaperdiniPublType2022:WorkingPaperArbeitspapierWorking paperKDSF (Pu37)SDNB:510SDNB:510510 Mathematik510 Mathematicsinstitution:unirostockinstitution:unirostockUniversität RostockUniversity of RostockUniversität RostockUniversität RostockUni.Rostockhttp://d-nb.info/gnd/38329-6institution:unirostock.mnfinstitution:unirostock.mnfMathematisch-Naturwissenschaftliche FakultätFaculty of Mathematics and Natural SciencesUniversität Rostock. Mathematisch-Naturwissenschaftliche FakultätMathematisch-Natur-<br />wissenschaftliche FakultätUni.Rostock.Fakultaet.MNFhttp://d-nb.info/gnd/2147083-2licenseinfo:worklicenseinfo:workWerkworklicenseinfo:work.rightsreservedlicenseinfo:work.rightsreservedalle Rechte vorbehaltenall rights reserved/creativecommons/r/reserved/0.9/88x31.png[DE-28]Urheberrechtsschutz 1.0$gRights Statements$uhttp://rightsstatements.org/vocab/InC/1.0/http://rightsstatements.org/vocab/InC/1.0/http://rightsstatements.org/vocab/InC/1.0/licenseinfo:depositlicenseinfo:depositVeröffentlichungsgenehmigungpermission to storelicenseinfo:deposit.rightsunirostocklicenseinfo:deposit.rightsunirostockRechteinhaber Universität Rostockrightsholder Rostock Universityaccesscondition:openaccessaccesscondition:openaccessfrei zugänglich (Open Access)open accesshttp://purl.org/coar/access_right/c_abf2OAfreeinfo:eu-repo/semantics/openAccess[DE-28]Open Access$gControlled Vocabulary for Access Rights$uhttp://purl.org/coar/access_right/c_abf2licenseinfo:metadatalicenseinfo:metadataLizenzen für Metadatenlicenseinfo:metadata.cc0licenseinfo:metadata.cc0Lizenz Metadaten: CC0license metadata: CC0/creativecommons/p/zero/1.0/88x31.pnghttps://creativecommons.org/publicdomain/zero/1.0/rfc5646:enrfc5646:enEnglischEnglishengengAproof of the theorem according to which every prime number possesses property BA proof of the theorem according to which every prime number possesses property Brosdok_document_0000027962-d3922713e50Christian ReiherChristian ReiherChristian ReiherChristian ReiherChristian ReiherRostockUniversity of Rostock, Institute of Mathematicsepub.workingpaperhttps://purl.uni-rostock.de/rosdok/id00005826urn:nbn:de:gbv:28-rosdok_id00005826-510.18453/rosdok_id00005826In the present thesis, we prove a conjecture belonging to a subbranch of additive combinatorics that is called combinatorial zero-sum theory. Denoting by p an arbitrary prime number, it has been known for about forty years that every sequence (P1, P2,..., P2p-1) consisting of 2p-1points from the affine plane Fp^2 possesses a non-empty subsequence the sum of whose elements equals zero. This fact has been first shown independently by Kruyswijk and Olson and is nowadays known to be an easy consequence of Alon´s combinatorial Nullstellensatz. A less obvious question asksfor a classification of all those sequences (P1, P2,..., P2p-2) of lenght 2p-2 whose only zero-sum subsequence is the empty one. This problem has been investigated by several researchers and in this respect a certain conjecture implying in particular that any such sequence contains p-2 equal points has attracted a great deal of attention in recent years. A precise version of this conjecture will be given below. By definition, the prime number p has property B if and only if it behaevs in accordance with the conjecture under discussion; by developing for the first time a powerful method for tackling such inverse problems over Fp^2, we prove the result alluded to in the title.20102010Preprints aus dem Institut für Mathematikrosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-810/10010-0001https://purl.uni-rostock.de/rosdok/id000058163255797-8Christian Reiherepub.workingpaper1 Reiher_proof_2010.pdf 271000 049267c915143bc936257512e8094932 rosdok_id000058261986691772Oau2026-10-132026-10-13T14:56:01ZrdaConverted from PICA to MODS using Pica2MODS XSLT Transformer 2.14-SNAPSHOT [SCM: "" "" ""] with mode 'DEFAULT'.WorkingpaperAproof of the theorem according to which every prime number possesses property BIn the present thesis, we prove a conjecture belonging to a subbranch of additive combinatorics that is called combinatorial zero-sum theory. Denoting by p an arbitrary prime number, it has been known for about forty years that every sequence (P1, P2,..., P2p-1) consisting of 2p-1points from the affine plane Fp^2 possesses a non-empty subsequence the sum of whose elements equals zero. This fact has been first shown independently by Kruyswijk and Olson and is nowadays known to be an easy consequence of Alon´s combinatorial Nullstellensatz. A less obvious question asksfor a classification of all those sequences (P1, P2,..., P2p-2) of lenght 2p-2 whose only zero-sum subsequence is the empty one. This problem has been investigated by several researchers and in this respect a certain conjecture implying in particular that any such sequence contains p-2 equal points has attracted a great deal of attention in recent years. A precise version of this conjecture will be given below. By definition, the prime number p has property B if and only if it behaevs in accordance with the conjecture under discussion; by developing for the first time a powerful method for tackling such inverse problems over Fp^2, we prove the result alluded to in the title.ChristianReiherVerfasserInauthttps://purl.uni-rostock.de/rosdok/id00005826urn:nbn:de:gbv:28-rosdok_id00005826-510.18453/rosdok_id00005826510 MathematikMathematisch-Naturwissenschaftliche Fakultätalle Rechte vorbehaltenRechteinhaber Universität Rostockfrei zugänglich (Open Access)Lizenz Metadaten: CC0en1 Online-Ressource (29 Seiten)2010University of Rostock, Institute of MathematicsRostockmonographic20102026Universitätsbibliothek RostockRostock2026Universitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00005826Christian Reiherrosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-810/10010-0001 2026-10-13T14:35:02.872Z 2026-10-13T14:58:35.723Z 2026-10-23T14:58:35.731Z editorKE {"identifier":"rosdok/id00005826","type":"local_id","additional":"","service":"MCRLocalID","created":"2026-10-13T14:35:02.885Z"} {"identifier":"urn:nbn:de:gbv:28-rosdok_id00005826-5","type":"dnbUrn","additional":"","service":"RosDokURN","created":"2026-10-13T14:35:02.892Z"} {"identifier":"https://purl.uni-rostock.de/rosdok/id00005826","type":"purl","additional":"","service":"RosDokPURL","created":"2026-10-13T14:35:02.897Z","registrationStarted":"2026-10-13T14:58:34.544Z"} {"identifier":"10.18453/rosdok_id00005826","type":"doi","additional":"","service":"RosDokDOI","created":"2026-10-13T14:35:02.901Z","registrationStarted":"2026-10-13T14:58:34.284Z","registered":"2026-10-13T14:58:35.721Z"} MCRJANITORfulltextfile/rosdok_document_0000027962/rosdok_derivate_0000229892/Reiher_proof_2010.pdfAproof of the theorem according to which every prime number possesses property BA proof of the theorem according to which every prime number possesses property Brosdok_document_0000027962-d3922713e50Christian ReiherChristian ReiherChristian ReiherChristian ReiherChristian ReiherRostockUniversity of Rostock, Institute of Mathematicsepub.workingpaperhttps://purl.uni-rostock.de/rosdok/id00005826urn:nbn:de:gbv:28-rosdok_id00005826-510.18453/rosdok_id00005826In the present thesis, we prove a conjecture belonging to a subbranch of additive combinatorics that is called combinatorial zero-sum theory. Denoting by p an arbitrary prime number, it has been known for about forty years that every sequence (P1, P2,..., P2p-1) consisting of 2p-1points from the affine plane Fp^2 possesses a non-empty subsequence the sum of whose elements equals zero. This fact has been first shown independently by Kruyswijk and Olson and is nowadays known to be an easy consequence of Alon´s combinatorial Nullstellensatz. A less obvious question asksfor a classification of all those sequences (P1, P2,..., P2p-2) of lenght 2p-2 whose only zero-sum subsequence is the empty one. This problem has been investigated by several researchers and in this respect a certain conjecture implying in particular that any such sequence contains p-2 equal points has attracted a great deal of attention in recent years. A precise version of this conjecture will be given below. By definition, the prime number p has property B if and only if it behaevs in accordance with the conjecture under discussion; by developing for the first time a powerful method for tackling such inverse problems over Fp^2, we prove the result alluded to in the title.20102010Preprints aus dem Institut für Mathematikrosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-810/10010-0001https://purl.uni-rostock.de/rosdok/id000058163255797-8Christian Reiher[xslt]Saxonrosdok_id00005826https://purl.uni-rostock.de/rosdok/id00005826198669177210.18453/rosdok_id00005826urn:nbn:de:gbv:28-rosdok_id00005826-5Christian ReiherReiher ChristianA proof of the theorem according to which every prime number possesses property BWorkingpaperworking paperUniversity of Rostock, Institute of Mathematics, 2010In the present thesis, we prove a conjecture belonging to a subbranch of additive combinatorics that is called combinatorial zero-sum theory. Denoting by p an arbitrary prime number, it has been known for about forty years that every sequence (P1, P2,..., P2p-1) consisting of 2p-1points from the…rosdok_id000058160010-000110/1Christian ReiherAproof of the theorem according to which every prime number possesses property BPreprints aus dem Institut für MathematikUniversitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00005826ChristianReiherVerfasserInaut[purl]https://purl.uni-rostock.de/rosdok/id00005826[urn]urn:nbn:de:gbv:28-rosdok_id00005826-5[doi]10.18453/rosdok_id00005826open_access20102010epoch:21th_centuryrfc5646:endoctype:epub.workingpaperaccesscondition:openaccessSDNB:510institution:unirostock.mnfstate:published