{"id":"https://openalex.org/W1975495852","doi":"https://doi.org/10.1090/s0025-5718-01-01381-3","title":"Thue\u2019s theorem and the diophantine equation \ud835\udc65\u00b2-\ud835\udc37\ud835\udc66\u00b2=\u00b1\ud835\udc41","display_name":"Thue\u2019s theorem and the diophantine equation \ud835\udc65\u00b2-\ud835\udc37\ud835\udc66\u00b2=\u00b1\ud835\udc41","publication_year":2001,"publication_date":"2001-09-17","ids":{"openalex":"https://openalex.org/W1975495852","doi":"https://doi.org/10.1090/s0025-5718-01-01381-3","mag":"1975495852"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-01-01381-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01381-3","pdf_url":"https://www.ams.org/mcom/2002-71-239/S0025-5718-01-01381-3/S0025-5718-01-01381-3.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":null,"license_id":null,"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":"bronze","oa_url":"https://www.ams.org/mcom/2002-71-239/S0025-5718-01-01381-3/S0025-5718-01-01381-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073013227","display_name":"Keith R. Matthews","orcid":"https://orcid.org/0000-0002-9564-1702"},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"The University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Keith Matthews","raw_affiliation_strings":["Department of Mathematics, University of Queensland, Brisbane, Australia, 4072"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Queensland, Brisbane, Australia, 4072","institution_ids":["https://openalex.org/I165143802"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073013227"],"corresponding_institution_ids":["https://openalex.org/I165143802"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.08024322,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"71","issue":"239","first_page":"1281","last_page":"1286"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9775000214576721,"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"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9746999740600586,"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/mathematics","display_name":"Mathematics","score":0.9178223609924316},{"id":"https://openalex.org/keywords/diophantine-equation","display_name":"Diophantine equation","score":0.863274097442627},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6445911526679993},{"id":"https://openalex.org/keywords/thue-equation","display_name":"Thue equation","score":0.593967854976654},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5076977014541626},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38951772451400757},{"id":"https://openalex.org/keywords/diophantine-set","display_name":"Diophantine set","score":0.37835636734962463},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3402346968650818}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9178223609924316},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.863274097442627},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6445911526679993},{"id":"https://openalex.org/C155635571","wikidata":"https://www.wikidata.org/wiki/Q2378270","display_name":"Thue equation","level":4,"score":0.593967854976654},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5076977014541626},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38951772451400757},{"id":"https://openalex.org/C40621787","wikidata":"https://www.wikidata.org/wiki/Q16251580","display_name":"Diophantine set","level":3,"score":0.37835636734962463},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3402346968650818},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-01-01381-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01381-3","pdf_url":"https://www.ams.org/mcom/2002-71-239/S0025-5718-01-01381-3/S0025-5718-01-01381-3.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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-01-01381-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01381-3","pdf_url":"https://www.ams.org/mcom/2002-71-239/S0025-5718-01-01381-3/S0025-5718-01-01381-3.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":null,"license_id":null,"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/W1975495852.pdf","grobid_xml":"https://content.openalex.org/works/W1975495852.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W620800051","https://openalex.org/W2006472498","https://openalex.org/W2057455622","https://openalex.org/W2274434947","https://openalex.org/W2796696350","https://openalex.org/W2894888219","https://openalex.org/W2907693862","https://openalex.org/W2914546856","https://openalex.org/W2986001730","https://openalex.org/W3145898342","https://openalex.org/W4235903219","https://openalex.org/W4246734892"],"related_works":["https://openalex.org/W2391619745","https://openalex.org/W2795416216","https://openalex.org/W2125060086","https://openalex.org/W4390811435","https://openalex.org/W606212217","https://openalex.org/W4295266667","https://openalex.org/W3145919182","https://openalex.org/W4385353872","https://openalex.org/W2372602505","https://openalex.org/W4366126351"],"abstract_inverted_index":{"A":[0],"constructive":[1],"version":[2],"of":[3,6,13],"a":[4],"theorem":[5],"Thue":[7],"is":[8],"used":[9],"to":[10],"provide":[11],"representations":[12],"certain":[14],"integers":[15],"as":[16],"<inline-formula":[17,50],"content-type=\"math/mathml\">":[18,51],"<mml:math":[19,52],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[20,53],"alttext=\"x":[21],"squared":[22],"minus":[23],"upper":[24],"D":[25,55],"y":[26],"squared\">":[27],"<mml:semantics>":[28,66],"<mml:mrow>":[29,67],"<mml:msup>":[30,38],"<mml:mi>x</mml:mi>":[31],"<mml:mn>2</mml:mn>":[32,40,70],"</mml:msup>":[33,41],"<mml:mo>":[34],"\u2212":[35],"</mml:mo>":[36],"<mml:mi>D</mml:mi>":[37,68],"<mml:mi>y</mml:mi>":[39],"</mml:mrow>":[42,79],"<mml:annotation":[43,80],"encoding=\"application/x-tex\">x^2-Dy^2</mml:annotation>":[44],"</mml:semantics>":[45,82],"</mml:math>":[46,83],"</inline-formula>":[47,84],",":[48],"where":[49],"alttext=\"upper":[54],"equals":[56],"2":[57],"comma":[58,60,62,64],"3":[59],"5":[61],"6":[63],"7\">":[65],"<mml:mo>=</mml:mo>":[69],"<mml:mo>,</mml:mo>":[71,73,75,77],"<mml:mn>3</mml:mn>":[72],"<mml:mn>5</mml:mn>":[74],"<mml:mn>6</mml:mn>":[76],"<mml:mn>7</mml:mn>":[78],"encoding=\"application/x-tex\">D=2,3,5,6,7</mml:annotation>":[81],".":[85]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}