{"id":"https://openalex.org/W2065918689","doi":"https://doi.org/10.1090/s0025-5718-08-02154-6","title":"A covering system with least modulus 25","display_name":"A covering system with least modulus 25","publication_year":2008,"publication_date":"2008-09-10","ids":{"openalex":"https://openalex.org/W2065918689","doi":"https://doi.org/10.1090/s0025-5718-08-02154-6","mag":"2065918689"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-08-02154-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02154-6","pdf_url":"https://www.ams.org/mcom/2009-78-266/S0025-5718-08-02154-6/S0025-5718-08-02154-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2009-78-266/S0025-5718-08-02154-6/S0025-5718-08-02154-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054716729","display_name":"D. Jason Gibson","orcid":null},"institutions":[{"id":"https://openalex.org/I110325482","display_name":"Eastern Kentucky University","ror":"https://ror.org/012xks909","country_code":"US","type":"education","lineage":["https://openalex.org/I110325482"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Donald Gibson","raw_affiliation_strings":["Eastern Kentucky University, 313 Wallace Building, 521 Lancaster Avenue, Richmond, Kentucky 40475-3102"],"affiliations":[{"raw_affiliation_string":"Eastern Kentucky University, 313 Wallace Building, 521 Lancaster Avenue, Richmond, Kentucky 40475-3102","institution_ids":["https://openalex.org/I110325482"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054716729"],"corresponding_institution_ids":["https://openalex.org/I110325482"],"apc_list":null,"apc_paid":null,"fwci":1.0677,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.74616956,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"78","issue":"266","first_page":"1127","last_page":"1146"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9998000264167786,"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":0.9998000264167786,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/congruence-relation","display_name":"Congruence relation","score":0.8085336685180664},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7970977425575256},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7350350618362427},{"id":"https://openalex.org/keywords/modulus","display_name":"Modulus","score":0.6454294323921204},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6257599592208862},{"id":"https://openalex.org/keywords/moduli","display_name":"Moduli","score":0.6188179850578308},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3414369225502014},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1704358160495758},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15480750799179077},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.054448068141937256}],"concepts":[{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.8085336685180664},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7970977425575256},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7350350618362427},{"id":"https://openalex.org/C193867417","wikidata":"https://www.wikidata.org/wiki/Q6889814","display_name":"Modulus","level":2,"score":0.6454294323921204},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6257599592208862},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.6188179850578308},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3414369225502014},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1704358160495758},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15480750799179077},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.054448068141937256},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-08-02154-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02154-6","pdf_url":"https://www.ams.org/mcom/2009-78-266/S0025-5718-08-02154-6/S0025-5718-08-02154-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.140.7950","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.7950","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/0000-000-00/S0025-5718-08-02154-6/S0025-5718-08-02154-6.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.146.2030","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.146.2030","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2009-78-266/S0025-5718-08-02154-6/S0025-5718-08-02154-6.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-08-02154-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02154-6","pdf_url":"https://www.ams.org/mcom/2009-78-266/S0025-5718-08-02154-6/S0025-5718-08-02154-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2065918689.pdf","grobid_xml":"https://content.openalex.org/works/W2065918689.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W159613098","https://openalex.org/W759014763","https://openalex.org/W1486265448","https://openalex.org/W1489006728","https://openalex.org/W1504038934","https://openalex.org/W1519568521","https://openalex.org/W1555475515","https://openalex.org/W1661292865","https://openalex.org/W1998084650","https://openalex.org/W2004580743","https://openalex.org/W2020505858","https://openalex.org/W2066637298","https://openalex.org/W2105352223","https://openalex.org/W2140057653","https://openalex.org/W2728028759","https://openalex.org/W4245003649","https://openalex.org/W6633444475","https://openalex.org/W6826660073"],"related_works":["https://openalex.org/W2778946875","https://openalex.org/W2023974151","https://openalex.org/W2163207601","https://openalex.org/W4301322097","https://openalex.org/W3049507786","https://openalex.org/W2103827354","https://openalex.org/W2590546754","https://openalex.org/W1486000879","https://openalex.org/W4388288403","https://openalex.org/W2032164205"],"abstract_inverted_index":{"A":[0,41],"collection":[1],"of":[2,31,44,53,77,99,144],"congruences":[3],"with":[4,91,110,135],"distinct":[5],"moduli,":[6],"each":[7,25],"greater":[8],"than":[9],"<inline-formula":[10,113],"content-type=\"math/mathml\">":[11,114],"<mml:math":[12,115],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[13,116],"alttext=\"1\">":[14],"<mml:semantics>":[15,118],"<mml:mn>1</mml:mn>":[16],"<mml:annotation":[17,120],"encoding=\"application/x-tex\">1</mml:annotation>":[18],"</mml:semantics>":[19,122],"</mml:math>":[20,123],"</inline-formula>":[21,124],",":[22],"such":[23],"that":[24,49,139],"integer":[26],"satisfies":[27],"at":[28,71,86],"least":[29,51,93,111],"one":[30],"the":[32,50,78,142,145],"congruences,":[33],"is":[34],"said":[35],"to":[36,73],"be":[37,58,74],"a":[38,54,107,129],"covering":[39,55,89,108],"system.":[40],"famous":[42],"conjecture":[43,62],"Erd\u00f6s":[45],"from":[46],"1950":[47],"states":[48],"modulus":[52,112],"system":[56,109],"can":[57],"arbitrarily":[59],"large.":[60],"This":[61],"remains":[63],"open":[64],"and,":[65],"in":[66,80,133],"its":[67],"full":[68],"strength,":[69],"appears":[70],"present":[72],"unattackable.":[75],"Most":[76],"effort":[79],"this":[81],"direction":[82],"has":[83],"been":[84],"aimed":[85],"explicitly":[87],"constructing":[88],"systems":[90],"large":[92],"modulus.":[94],"Improving":[95],"upon":[96],"previous":[97],"results":[98,138],"Churchhouse,":[100],"Krukenberg,":[101],"Choi,":[102],"and":[103],"Morikawa,":[104],"we":[105],"construct":[106],"alttext=\"25\">":[117],"<mml:mn>25</mml:mn>":[119],"encoding=\"application/x-tex\">25</mml:annotation>":[121],".":[125],"The":[126],"construction":[127],"involves":[128],"large-scale":[130],"computer":[131],"search,":[132],"conjunction":[134],"two":[136],"general":[137],"considerably":[140],"reduce":[141],"complexity":[143],"search.":[146]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}