{"id":"https://openalex.org/W2974328897","doi":"https://doi.org/10.1080/00029890.2019.1632628","title":"Perfect Squares as Concatenation of Consecutive Integers","display_name":"Perfect Squares as Concatenation of Consecutive Integers","publication_year":2019,"publication_date":"2019-09-14","ids":{"openalex":"https://openalex.org/W2974328897","doi":"https://doi.org/10.1080/00029890.2019.1632628","mag":"2974328897"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2019.1632628","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2019.1632628","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,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"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"},"type":"article","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/A5007752336","display_name":"Florian Luca","orcid":"https://orcid.org/0000-0003-1321-4422"},"institutions":[{"id":"https://openalex.org/I192619145","display_name":"University of the Witwatersrand","ror":"https://ror.org/03rp50x72","country_code":"ZA","type":"education","lineage":["https://openalex.org/I192619145"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"Florian Luca","raw_affiliation_strings":["School of Maths, Wits University, Private Bag, Wits 2050, Johannesburg, South Africa"],"affiliations":[{"raw_affiliation_string":"School of Maths, Wits University, Private Bag, Wits 2050, Johannesburg, South Africa","institution_ids":["https://openalex.org/I192619145"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021290362","display_name":"Pantelimon St\u0103nic\u0103","orcid":"https://orcid.org/0000-0002-8622-7120"},"institutions":[{"id":"https://openalex.org/I35364215","display_name":"Naval Postgraduate School","ror":"https://ror.org/033yfkj90","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I3130687028","https://openalex.org/I35364215"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pantelimon St\u0103nic\u0103","raw_affiliation_strings":["Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943, USA"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943, USA","institution_ids":["https://openalex.org/I35364215"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007752336"],"corresponding_institution_ids":["https://openalex.org/I192619145"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.23788638,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"126","issue":"8","first_page":"728","last_page":"734"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9972000122070312,"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":0.9972000122070312,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9914000034332275,"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/concatenation","display_name":"Concatenation (mathematics)","score":0.9677139520645142},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6259875297546387},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.5727071166038513},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.5672896504402161},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5399631857872009},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3983163833618164},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3610789179801941},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3278637230396271},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11160197854042053},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10359328985214233}],"concepts":[{"id":"https://openalex.org/C87619178","wikidata":"https://www.wikidata.org/wiki/Q126002","display_name":"Concatenation (mathematics)","level":2,"score":0.9677139520645142},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6259875297546387},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.5727071166038513},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5672896504402161},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5399631857872009},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3983163833618164},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3610789179801941},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3278637230396271},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11160197854042053},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10359328985214233}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00029890.2019.1632628","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2019.1632628","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,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"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":"pmh:oai:calhoun.nps.edu:10945/64438","is_oa":false,"landing_page_url":"https://hdl.handle.net/10945/64438","pdf_url":null,"source":{"id":"https://openalex.org/S4306400952","display_name":"Calhoun: The Naval Postgraduate School Institutional Archive (Naval Postgraduate School)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35364215","host_organization_name":"Naval Postgraduate School","host_organization_lineage":["https://openalex.org/I35364215"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2373577936","https://openalex.org/W4221148444","https://openalex.org/W4387678054","https://openalex.org/W2389596151","https://openalex.org/W3095575180","https://openalex.org/W4306784355","https://openalex.org/W2169308097","https://openalex.org/W3091984855","https://openalex.org/W2946585142","https://openalex.org/W3120719177"],"abstract_inverted_index":{"We":[0],"find":[1],"an":[2],"infinite":[3],"family":[4],"of":[5],"positive":[6],"integers":[7],"a":[8,12,14,26,30],"such":[9,36],"that":[10,28],"concatenating":[11],"and":[13,33],"\u2013":[15],"1":[16],"in":[17,25],"base":[18],"10":[19],"(from":[20],"left":[21],"to":[22],"right)":[23],"results":[24],"number":[27],"is":[29],"perfect":[31],"square":[32],"estimates":[34],"for":[35],"concatenations.":[37]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}