{"id":"https://openalex.org/W2025053931","doi":"https://doi.org/10.1142/s0218196798000296","title":"A Greatest Common Divisor Algorithm","display_name":"A Greatest Common Divisor Algorithm","publication_year":1998,"publication_date":"1998-10-01","ids":{"openalex":"https://openalex.org/W2025053931","doi":"https://doi.org/10.1142/s0218196798000296","mag":"2025053931"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196798000296","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196798000296","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5030270352","display_name":"Ari Belenkiy","orcid":"https://orcid.org/0000-0001-9151-7985"},"institutions":[{"id":"https://openalex.org/I13955877","display_name":"Bar-Ilan University","ror":"https://ror.org/03kgsv495","country_code":"IL","type":"education","lineage":["https://openalex.org/I13955877"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Ari Belenkiy","raw_affiliation_strings":["Mathematics and Computer Science Department, Bar-Ilan University, Ramat-Gan, Israel","Mathematics and Computer Science Department, Bar-Ilan University, Ramat-Gan, Israel#TAB#"],"affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science Department, Bar-Ilan University, Ramat-Gan, Israel","institution_ids":["https://openalex.org/I13955877"]},{"raw_affiliation_string":"Mathematics and Computer Science Department, Bar-Ilan University, Ramat-Gan, Israel#TAB#","institution_ids":["https://openalex.org/I13955877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078092920","display_name":"Raimundas Vid\u016bnas","orcid":"https://orcid.org/0000-0002-9124-7804"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Raimundas Vidunas","raw_affiliation_strings":["Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands","Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]},{"raw_affiliation_string":"Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands#TAB#","institution_ids":["https://openalex.org/I169381384"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030270352"],"corresponding_institution_ids":["https://openalex.org/I13955877"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.15638862,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"08","issue":"05","first_page":"617","last_page":"623"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.8978999853134155,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.8978999853134155,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.855400025844574,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.8296999931335449,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8694057464599609},{"id":"https://openalex.org/keywords/greatest-common-divisor","display_name":"Greatest common divisor","score":0.8477964401245117},{"id":"https://openalex.org/keywords/divisor","display_name":"Divisor (algebraic geometry)","score":0.6693616509437561},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6285387873649597},{"id":"https://openalex.org/keywords/euclidean-algorithm","display_name":"Euclidean algorithm","score":0.5965410470962524},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5899533033370972},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5311794281005859},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4820905029773712},{"id":"https://openalex.org/keywords/rational-number","display_name":"Rational number","score":0.43200933933258057},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40602636337280273},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40402835607528687},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4012739658355713},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34470880031585693},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12066277861595154}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8694057464599609},{"id":"https://openalex.org/C125257309","wikidata":"https://www.wikidata.org/wiki/Q131752","display_name":"Greatest common divisor","level":2,"score":0.8477964401245117},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.6693616509437561},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6285387873649597},{"id":"https://openalex.org/C98371066","wikidata":"https://www.wikidata.org/wiki/Q230848","display_name":"Euclidean algorithm","level":2,"score":0.5965410470962524},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5899533033370972},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5311794281005859},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4820905029773712},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.43200933933258057},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40602636337280273},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40402835607528687},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4012739658355713},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34470880031585693},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12066277861595154},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196798000296","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196798000296","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:pure.rug.nl:publications/97ae1383-7dd2-4161-9bdc-fa2780c7ce25","is_oa":false,"landing_page_url":"https://research.rug.nl/en/publications/97ae1383-7dd2-4161-9bdc-fa2780c7ce25","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Belenkiy, A & Vidunas, R 1998, 'A greatest common divisor algorithm', International journal of algebra and computation, vol. 8, no. 5, pp. 617-623.","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5099999904632568}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2014355030","https://openalex.org/W4253984331"],"related_works":["https://openalex.org/W3047275406","https://openalex.org/W2115468732","https://openalex.org/W1993482309","https://openalex.org/W2510351432","https://openalex.org/W1550016006","https://openalex.org/W4256203780","https://openalex.org/W2492714232","https://openalex.org/W283968525","https://openalex.org/W2953831318","https://openalex.org/W4250443881"],"abstract_inverted_index":{"Algorithms":[0],"of":[1,3,9,42,73,101,122,128,134,137],"computation":[2],"the":[4,30,65,82,86,135],"Greatest":[5],"Common":[6],"Divisor":[7],"(GCD)":[8],"two":[10,98],"integers":[11],"play":[12],"a":[13,69,114,126,129,146,153],"principal":[14],"role":[15],"in":[16,55],"all":[17],"computational":[18],"systems":[19],"dealing":[20],"with":[21,68,77,118,125],"rational":[22],"arithmetic.":[23],"The":[24,132],"simplest":[25],"one":[26,120],"(Euclidean)":[27],"is":[28,61],"not":[29],"best":[31],"for":[32,45],"large":[33,74],"numbers":[34,75,102,123],"(see":[35],"D.":[36,52],"E.":[37,89],"Knuth's":[38],"book":[39],"\"The":[40],"Art":[41],"Computer":[43],"Programming\"":[44],"details).":[46],"One":[47],"improvement":[48],"was":[49],"suggested":[50],"by":[51],"H.":[53],"Lehmer":[54],"1938":[56],"who":[57],"noticed":[58],"that":[59,93],"it":[60],"possible":[62],"to":[63,116],"run":[64],"Euclidean":[66],"algorithm":[67,95],"few":[70],"leading":[71],"digits":[72],"and,":[76],"some":[78],"care,":[79],"still":[80],"obtain":[81],"correct":[83],"answer.":[84],"In":[85],"70's":[87],"G.":[88],"Collins":[90,112],"pointed":[91],"out":[92],"Lehmer's":[94],"simultaneously":[96],"analyzed":[97],"similar":[99,147],"sequences":[100],"and":[103,151,155],"hence":[104],"did":[105],"twice":[106],"as":[107,110],"much":[108],"work":[109,117],"necessary.":[111],"found":[113],"way":[115],"only":[119],"sequence":[121],"together":[124],"verification":[127],"certain":[130],"inequality.":[131],"proof":[133,157],"validity":[136],"this":[138],"inequality":[139,150],"is,":[140],"perhaps,":[141],"too":[142],"complicated.":[143],"We":[144],"present":[145],"but":[148],"softer":[149],"give":[152],"short":[154],"simple":[156],"thereof.":[158]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
