{"id":"https://openalex.org/W2318283572","doi":"https://doi.org/10.1080/00029890.1994.12004581","title":"Variations on Wolstenholme's Theorem","display_name":"Variations on Wolstenholme's Theorem","publication_year":1994,"publication_date":"1994-12-01","ids":{"openalex":"https://openalex.org/W2318283572","doi":"https://doi.org/10.1080/00029890.1994.12004581","mag":"2318283572"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.1994.12004581","doi":"https://doi.org/10.1080/00029890.1994.12004581","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.1994.12004581","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific","dongbi-b","jufo-1","norway-1","poland-40","russia-white-list-4","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038105329","display_name":"Emr\u00e9 Alkan","orcid":"https://orcid.org/0000-0003-1594-041X","observed_orcids":["https://orcid.org/0000-0003-1594-041X"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Emre Alkan","raw_affiliation_strings":["(Undergraduate Student) Department of Mathematics Bosphorus University Istanbul, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"(Undergraduate Student) Department of Mathematics Bosphorus University Istanbul, Turkey","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5038105329"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7561,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.54075971,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"101","issue":"10","first_page":"1001","last_page":"1001"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9545999765396118,"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":0.9545999765396118,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.026900000870227814,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.011900000274181366,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/wolstenholme-s-theorem","display_name":"Wolstenholme's theorem","score":0.9990000128746033},{"id":"https://openalex.org/keywords/harmonic-series","display_name":"harmonic series","score":0.8180000185966492},{"id":"https://openalex.org/keywords/harmonic-numbers","display_name":"harmonic numbers","score":0.7319999933242798},{"id":"https://openalex.org/keywords/congruences","display_name":"congruences","score":0.6949999928474426},{"id":"https://openalex.org/keywords/prime-numbers","display_name":"prime numbers","score":0.4869999885559082},{"id":"https://openalex.org/keywords/divisibility","display_name":"divisibility","score":0.4690000116825104}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46208521723747253},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.44001075625419617}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00029890.1994.12004581","doi":"https://doi.org/10.1080/00029890.1994.12004581","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.1994.12004581","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific","dongbi-b","jufo-1","norway-1","poland-40","russia-white-list-4","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},{"id":"doi:10.2307/2975168","doi":"https://doi.org/10.2307/2975168","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2975168","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific","dongbi-b","jufo-1","norway-1","poland-40","russia-white-list-4","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2027875058","https://openalex.org/W3175367423"],"related_works":["https://openalex.org/W2333897907","https://openalex.org/W2333893880","https://openalex.org/W4234801545","https://openalex.org/W2091204563","https://openalex.org/W3176304734","https://openalex.org/W2330363901","https://openalex.org/W2799527880","https://openalex.org/W1638972840","https://openalex.org/W2314935526","https://openalex.org/W4246564171"],"abstract_inverted_index":{"(1994).":[0],"Variations":[1],"on":[2],"Wolstenholme's":[3],"Theorem.":[4],"The":[5],"American":[6],"Mathematical":[7],"Monthly:":[8],"Vol.":[9],"101,":[10],"No.":[11],"10,":[12],"pp.":[13],"1001-1004.":[14]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2016-06-24T00:00:00"}
