{"id":"https://openalex.org/W3134610798","doi":null,"title":"Solving Brocard's Problem","display_name":"Solving Brocard's Problem","publication_year":2021,"publication_date":"2021-03-01","ids":{"openalex":"https://openalex.org/W3134610798","mag":"3134610798"},"language":"en","primary_location":{"id":"mag:3134610798","doi":null,"is_oa":false,"landing_page_url":"https://vixra.org/pdf/2103.0038v1.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2883122597","display_name":"viXra","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"viXra","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"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/A5041263423","display_name":"Kurmet Sultan","orcid":"https://orcid.org/0000-0002-7852-8994","observed_orcids":["https://orcid.org/0000-0002-7852-8994"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kurmet Sultan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5041263423"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9193999767303467,"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":0.9193999767303467,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.03550000116229057,"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"}},{"id":"https://openalex.org/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":0.020500000566244125,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/brocard-s-problem","display_name":"Brocard's problem","score":0.9990000128746033},{"id":"https://openalex.org/keywords/factorials","display_name":"factorials","score":0.8240000009536743},{"id":"https://openalex.org/keywords/diophantine-equations","display_name":"Diophantine equations","score":0.8149999976158142},{"id":"https://openalex.org/keywords/products-of-consecutive-integers","display_name":"products of consecutive integers","score":0.5479999780654907},{"id":"https://openalex.org/keywords/impossibility-proofs","display_name":"impossibility proofs","score":0.6859999895095825}],"concepts":[{"id":"https://openalex.org/C2776261394","wikidata":"https://www.wikidata.org/wiki/Q315562","display_name":"Impossibility","level":2,"score":0.8645362257957458},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5528464317321777},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5405420660972595},{"id":"https://openalex.org/C2776608160","wikidata":"https://www.wikidata.org/wiki/Q4785462","display_name":"Natural (archaeology)","level":2,"score":0.4777090549468994},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4644603133201599},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4349871873855591},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34579792618751526},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34018373489379883},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.12941628694534302},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.06931591033935547},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.05404865741729736},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.05404108762741089},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:3134610798","doi":null,"is_oa":false,"landing_page_url":"https://vixra.org/pdf/2103.0038v1.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2883122597","display_name":"viXra","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"viXra","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4401197680","https://openalex.org/W6922455960","https://openalex.org/W7166330849","https://openalex.org/W2107929630","https://openalex.org/W7147244339","https://openalex.org/W6912084305","https://openalex.org/W6959910325","https://openalex.org/W3112238144","https://openalex.org/W2885094398","https://openalex.org/W2763922638"],"abstract_inverted_index":{"The":[0],"article":[1],"provides":[2],"a":[3,24,31],"solution":[4],"to":[5],"Brocard's":[6],"problem":[7],"by":[8],"proving":[9],"the":[10,17,20],"impossibility":[11],"of":[12,19,26,33],"representing":[13],"other":[14],"factorials,":[15],"with":[16,30],"exception":[18],"known":[21],"three,":[22],"as":[23],"product":[25],"two":[27],"natural":[28],"numbers":[29],"difference":[32],"2.":[34]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2021-03-15T00:00:00"}
