{"id":"https://openalex.org/W26987041","doi":null,"title":"On the resolution of simultaneous Pell equations","display_name":"On the resolution of simultaneous Pell equations","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W26987041","mag":"26987041"},"language":"en","primary_location":{"id":"pmh:oai:publicatio.nyme.hu:313","doi":null,"is_oa":true,"landing_page_url":"http://publicatio.nyme.hu/313/1/AMI_34_from77to87.pdf","pdf_url":"http://publicatio.nyme.hu/313/1/AMI_34_from77to87.pdf","source":{"id":"https://openalex.org/S4306402309","display_name":"\u00dcdv\u00f6z\u00f6lj\u00fck a Publicatio oldal\u00e1n (University of West Hungary)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I85686399","host_organization_name":"University of Sopron","host_organization_lineage":["https://openalex.org/I85686399"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Cikk"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://publicatio.nyme.hu/313/1/AMI_34_from77to87.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069177105","display_name":"L\u00e1szl\u00f3 Szalay","orcid":"https://orcid.org/0000-0002-4582-6100","observed_orcids":["https://orcid.org/0000-0002-4582-6100"]},"institutions":[{"id":"https://openalex.org/I85686399","display_name":"University of Sopron","ror":"https://ror.org/05nj7my03","country_code":"HU","type":"education","lineage":["https://openalex.org/I85686399"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"L\u00e1szl\u00f3 Szalay","raw_affiliation_strings":["University of West hungary"],"raw_orcid":"https://orcid.org/0000-0002-4582-6100","affiliations":[{"raw_affiliation_string":"University of West hungary","institution_ids":["https://openalex.org/I85686399"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069177105"],"corresponding_institution_ids":["https://openalex.org/I85686399"],"apc_list":null,"apc_paid":null,"fwci":1.4849,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.76910201,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":97},"biblio":{"volume":"34","issue":null,"first_page":"77","last_page":"87"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.98580002784729,"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"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.98580002784729,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.006500000134110451,"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/T11166","display_name":"Analytic Number Theory Research","score":0.0010999999940395355,"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/pell-s-equation","display_name":"Pell's equation","score":0.47600001096725464},{"id":"https://openalex.org/keywords/diophantine-equations","display_name":"Diophantine equations","score":0.7129999995231628},{"id":"https://openalex.org/keywords/magma-implementation","display_name":"Magma implementation","score":0.699999988079071},{"id":"https://openalex.org/keywords/quadratic-forms","display_name":"quadratic forms","score":0.5329999923706055},{"id":"https://openalex.org/keywords/number-theory","display_name":"number theory","score":0.4560000002384186}],"concepts":[{"id":"https://openalex.org/C183222429","wikidata":"https://www.wikidata.org/wiki/Q42278","display_name":"Magma","level":3,"score":0.6463581919670105},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.4850839674472809},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.48266246914863586},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4462668299674988},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4432436227798462},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4192884564399719},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3592493236064911},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.22301414608955383},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21882715821266174},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19241008162498474},{"id":"https://openalex.org/C165205528","wikidata":"https://www.wikidata.org/wiki/Q83371","display_name":"Seismology","level":1,"score":0.0},{"id":"https://openalex.org/C120806208","wikidata":"https://www.wikidata.org/wiki/Q8072","display_name":"Volcano","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:publicatio.nyme.hu:313","doi":null,"is_oa":true,"landing_page_url":"http://publicatio.nyme.hu/313/1/AMI_34_from77to87.pdf","pdf_url":"http://publicatio.nyme.hu/313/1/AMI_34_from77to87.pdf","source":{"id":"https://openalex.org/S4306402309","display_name":"\u00dcdv\u00f6z\u00f6lj\u00fck a Publicatio oldal\u00e1n (University of West Hungary)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I85686399","host_organization_name":"University of Sopron","host_organization_lineage":["https://openalex.org/I85686399"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Cikk"},{"id":"pmh:oai:publikacio.uni-eszterhazy.hu:3034","doi":null,"is_oa":true,"landing_page_url":"http://publikacio.uni-eszterhazy.hu/3034/1/AMI_34_from77to87.pdf","pdf_url":"http://publikacio.uni-eszterhazy.hu/3034/1/AMI_34_from77to87.pdf","source":{"id":"https://openalex.org/S4306400765","display_name":"Acta Biologica Plantarum Agriensis (Eszterh\u00e1zy K\u00e1roly University, Hungary)","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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Foly\u00f3iratcikk"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.94.1929","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.94.1929","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/AMI/2007/ami2007-szalay.pdf","raw_type":"text"},{"id":"mag:26987041","doi":null,"is_oa":false,"landing_page_url":"http://ami.ektf.hu/uploads/papers/finalpdf/AMI_34_from77to87.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:publicatio.nyme.hu:313","doi":null,"is_oa":true,"landing_page_url":"http://publicatio.nyme.hu/313/1/AMI_34_from77to87.pdf","pdf_url":"http://publicatio.nyme.hu/313/1/AMI_34_from77to87.pdf","source":{"id":"https://openalex.org/S4306402309","display_name":"\u00dcdv\u00f6z\u00f6lj\u00fck a Publicatio oldal\u00e1n (University of West Hungary)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I85686399","host_organization_name":"University of Sopron","host_organization_lineage":["https://openalex.org/I85686399"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Cikk"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4000145918","display_name":null,"funder_award_id":"51125006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4747210428","display_name":null,"funder_award_id":"61376056","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7959026768","display_name":null,"funder_award_id":"91122034","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W26987041.pdf","grobid_xml":"https://content.openalex.org/works/W26987041.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W41450536","https://openalex.org/W380261967","https://openalex.org/W1575761830","https://openalex.org/W1969609479","https://openalex.org/W1969659369","https://openalex.org/W1970456472","https://openalex.org/W1975413201","https://openalex.org/W1987193344","https://openalex.org/W1999714276","https://openalex.org/W2029775181","https://openalex.org/W2063934242","https://openalex.org/W2090883175","https://openalex.org/W2182628601","https://openalex.org/W2326825343","https://openalex.org/W2461996928","https://openalex.org/W2591114074","https://openalex.org/W3203668817"],"related_works":["https://openalex.org/W2468550154","https://openalex.org/W7071919678","https://openalex.org/W2331639635","https://openalex.org/W7170483744","https://openalex.org/W2123174602","https://openalex.org/W2087886281","https://openalex.org/W2971455155","https://openalex.org/W2746014900","https://openalex.org/W1994024219","https://openalex.org/W3035319828"],"abstract_inverted_index":{"We":[0],"descibe":[1],"an":[2],"alternative":[3],"procedure":[4,44],"for":[5],"solving":[6],"automatically":[7],"simultaneous":[8],"Pell":[9],"equations":[10],"with":[11],"relatively":[12],"small":[13],"coefficients.The":[14],"word":[15],"\"automatically\"":[16],"means":[17],"to":[18],"indicate":[19],"that":[20],"the":[21,41,47,51],"algorithm":[22],"can":[23],"be":[24],"implemented":[25],"in":[26],"Magma.Numerous":[27],"famous":[28],"examples":[29],"are":[30],"verified":[31],"and":[32],"a":[33],"new":[34],"theorem":[35],"is":[36],"proved":[37],"by":[38],"running":[39],"simply":[40],"corresponding":[42],"Magma":[43],"requires":[45],"only":[46],"six":[48],"coefficients":[49],"of":[50],"system":[52],"a1x":[53],"2":[54,57,61,64],"+":[55,62],"b1y":[56],"=":[58,65],"c1,":[59],"a2x":[60],"b2z":[63],"c2.":[66]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}