{"id":"https://openalex.org/W2054575177","doi":"https://doi.org/10.1215/00294527-2008-021","title":"The Sum of Irreducible Fractions with Consecutive Denominators Is Never an Integer in PA-","display_name":"The Sum of Irreducible Fractions with Consecutive Denominators Is Never an Integer in PA-","publication_year":2008,"publication_date":"2008-10-01","ids":{"openalex":"https://openalex.org/W2054575177","doi":"https://doi.org/10.1215/00294527-2008-021","mag":"2054575177"},"language":"en","primary_location":{"id":"doi:10.1215/00294527-2008-021","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2008-021","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-49/issue-4/The-Sum-of-Irreducible-Fractions-with-Consecutive-Denominators-Is-Never/10.1215/00294527-2008-021.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-49/issue-4/The-Sum-of-Irreducible-Fractions-with-Consecutive-Denominators-Is-Never/10.1215/00294527-2008-021.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038599115","display_name":"Victor Pambuccian","orcid":"https://orcid.org/0000-0003-2263-1471"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Victor Pambuccian","raw_affiliation_strings":["New College of Interdisciplinary Arts & Sciences Arizona State University-West Campus PO Box 37100 Phoenix AZ 85069-7100 USA","NCIAS: Humanities, Arts and Cultural Studies, School of (SHARCS)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"New College of Interdisciplinary Arts & Sciences Arizona State University-West Campus PO Box 37100 Phoenix AZ 85069-7100 USA","institution_ids":["https://openalex.org/I55732556"]},{"raw_affiliation_string":"NCIAS: Humanities, Arts and Cultural Studies, School of (SHARCS)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038599115"],"corresponding_institution_ids":["https://openalex.org/I55732556"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.14296814,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"49","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9811000227928162,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9811000227928162,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9803000092506409,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9778000116348267,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7714155912399292},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6890835762023926},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6549910306930542},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.599596381187439},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4771275520324707},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.43714383244514465},{"id":"https://openalex.org/keywords/number-theory","display_name":"Number theory","score":0.41463011503219604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06946757435798645}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7714155912399292},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6890835762023926},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6549910306930542},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.599596381187439},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4771275520324707},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.43714383244514465},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.41463011503219604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06946757435798645},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1215/00294527-2008-021","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2008-021","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-49/issue-4/The-Sum-of-Irreducible-Fractions-with-Consecutive-Denominators-Is-Never/10.1215/00294527-2008-021.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1224257540","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1224257540","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1215/00294527-2008-021","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2008-021","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-49/issue-4/The-Sum-of-Irreducible-Fractions-with-Consecutive-Denominators-Is-Never/10.1215/00294527-2008-021.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2054575177.pdf","grobid_xml":"https://content.openalex.org/works/W2054575177.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W142824415","https://openalex.org/W1601654835","https://openalex.org/W2603211935","https://openalex.org/W2795886238"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W178365807","https://openalex.org/W1555836633","https://openalex.org/W4240676090","https://openalex.org/W2081441417","https://openalex.org/W1970375080","https://openalex.org/W4386544785","https://openalex.org/W16157476","https://openalex.org/W1522717445","https://openalex.org/W2116374711"],"abstract_inverted_index":{"Two":[0],"results":[1],"of":[2],"elementary":[3],"number":[4],"theory,":[5],"going":[6],"back":[7],"to":[8,41],"K\u00fcrsch\u00e1k":[9],"and":[10,27],"Nagell,":[11],"stating":[12],"that":[13],"the":[14],"sums":[15],"\u2211i=1":[16],"k":[17,29],"mi":[18,23,25],"n+i":[19],"(with":[20,32],"k\u22651,":[21],"(":[22],",n+i)=1,":[24],"<n+i)":[26],"\u2211i=0":[28],"1":[30],"m+in":[31],"n,m,k":[33],"positive":[34],"integers)":[35],"are":[36,39],"never":[37],"integers,":[38],"shown":[40],"hold":[42],"in":[43],"PA-":[44],",":[45],"a":[46],"very":[47],"weak":[48],"arithmetic,":[49],"whose":[50],"axiom":[51],"system":[52],"has":[53],"no":[54],"induction":[55],"axiom.":[56]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
