{"id":"https://openalex.org/W1999714276","doi":"https://doi.org/10.1090/s0025-5718-98-00918-1","title":"Solving constrained Pell equations","display_name":"Solving constrained Pell equations","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1999714276","doi":"https://doi.org/10.1090/s0025-5718-98-00918-1","mag":"1999714276"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-98-00918-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00918-1","pdf_url":"https://www.ams.org/mcom/1998-67-222/S0025-5718-98-00918-1/S0025-5718-98-00918-1.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/1998-67-222/S0025-5718-98-00918-1/S0025-5718-98-00918-1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036080574","display_name":"Kiran S. Kedlaya","orcid":"https://orcid.org/0000-0001-8700-8758"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Kiran Kedlaya","raw_affiliation_strings":["Department of Mathematics  Princeton University  Princeton, New Jersey 08544","Department of Mathematics, Princeton University, Princeton, New Jersey, 08544#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics  Princeton University  Princeton, New Jersey 08544","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Department of Mathematics, Princeton University, Princeton, New Jersey, 08544#TAB#","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5036080574"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":4.6713,"has_fulltext":true,"cited_by_count":52,"citation_normalized_percentile":{"value":0.95419365,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"67","issue":"222","first_page":"833","last_page":"842"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9988999962806702,"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":0.9988999962806702,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9918000102043152,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.988099992275238,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6185911893844604},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3816509246826172},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37264320254325867}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6185911893844604},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3816509246826172},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37264320254325867}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-98-00918-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00918-1","pdf_url":"https://www.ams.org/mcom/1998-67-222/S0025-5718-98-00918-1/S0025-5718-98-00918-1.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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.106.9123","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.106.9123","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/1998-67-222/S0025-5718-98-00918-1/S0025-5718-98-00918-1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.879","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.879","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/journals/mcom/1998-67-222/S0025-5718-98-00918-1/S0025-5718-98-00918-1.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-98-00918-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00918-1","pdf_url":"https://www.ams.org/mcom/1998-67-222/S0025-5718-98-00918-1/S0025-5718-98-00918-1.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/W1999714276.pdf","grobid_xml":"https://content.openalex.org/works/W1999714276.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1542908046","https://openalex.org/W1575761830","https://openalex.org/W1817451992","https://openalex.org/W1987193344","https://openalex.org/W1991109318","https://openalex.org/W2022784678","https://openalex.org/W2049493613","https://openalex.org/W2090883175","https://openalex.org/W2119982852","https://openalex.org/W2123174602","https://openalex.org/W2169851573","https://openalex.org/W2297456208","https://openalex.org/W2317659985","https://openalex.org/W2487302930","https://openalex.org/W2591114074","https://openalex.org/W2592184324","https://openalex.org/W4235903219","https://openalex.org/W4242002877","https://openalex.org/W4242037478","https://openalex.org/W4245909385"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2003465964","https://openalex.org/W3107474891","https://openalex.org/W303980170","https://openalex.org/W2351491280","https://openalex.org/W2386767533","https://openalex.org/W2371447506","https://openalex.org/W2333698505"],"abstract_inverted_index":{"Consider":[0],"the":[1,121,137,140,150,153],"system":[2],"of":[3,134,139],"Diophantine":[4],"equations":[5],"<inline-formula":[6,45,87,155,202],"content-type=\"math/mathml\">":[7,46,88,156,203],"<mml:math":[8,47,89,157,204],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[9,48,90,158,205],"alttext=\"x":[10],"squared":[11,15,169],"minus":[12],"a":[13,101,126,257],"y":[14,54,164,168,211],"equals":[16,56,166,213],"b\">":[17],"<mml:semantics>":[18,59,93,172,218],"<mml:mrow>":[19,60,173,219],"<mml:msup>":[20,28,70,184],"<mml:mi>x</mml:mi>":[21,64,177,223,230],"<mml:mn>2</mml:mn>":[22,30,74,186],"</mml:msup>":[23,31,76,187],"<mml:mo>":[24],"\u2212":[25],"</mml:mo>":[26],"<mml:mi>a</mml:mi>":[27],"<mml:mi>y</mml:mi>":[29,66,179,185,225],"<mml:mo>=</mml:mo>":[32,69,182,228],"<mml:mi>b</mml:mi>":[33],"</mml:mrow>":[34,75,77,190,233],"<mml:annotation":[35,78,95,191,234],"encoding=\"application/x-tex\">x^2":[36],"-":[37],"ay^2":[38],"=":[39,80,194,237],"b</mml:annotation>":[40],"</mml:semantics>":[41,82,97,198,241],"</mml:math>":[42,83,98,199,242],"</inline-formula>":[43,84,99,200,243],",":[44,85,244],"alttext=\"upper":[49,91,159,206],"P":[50,160,207],"left-parenthesis":[51,161,208],"x":[52,162,209,215],"comma":[53,163,210],"right-parenthesis":[55,165,212],"z":[57],"squared\">":[58],"<mml:mi>P</mml:mi>":[61,94,174,220],"<mml:mo":[62,67,175,180,221,226],"stretchy=\"false\">(</mml:mo>":[63,176,222],"<mml:mo>,</mml:mo>":[65,178,224],"stretchy=\"false\">)</mml:mo>":[68,181,227],"<mml:mi>z</mml:mi>":[71],"<mml:mrow":[72],"class=\"MJX-TeXAtom-ORD\">":[73],"encoding=\"application/x-tex\">P(x,y)":[79],"z^{2}</mml:annotation>":[81],"where":[86],"P\">":[92],"encoding=\"application/x-tex\">P</mml:annotation>":[96],"is":[100],"given":[102],"integer":[103,122,250],"polynomial.":[104],"Historically,":[105],"such":[106,146],"systems":[107],"have":[108],"been":[109],"analyzed":[110],"by":[111],"using":[112],"Baker\u2019s":[113],"method":[114],"to":[115,152],"produce":[116],"an":[117,132,253],"upper":[118],"bound":[119],"on":[120,131,252],"solutions.":[123],"We":[124,148],"present":[125],"general":[127],"elementary":[128],"approach,":[129],"based":[130],"idea":[133],"Cohn":[135],"and":[136,201],"theory":[138],"Pell":[141],"equation,":[142],"that":[143],"solves":[144],"many":[145],"systems.":[147],"apply":[149],"approach":[151],"cases":[154],"c":[167,214],"plus":[170,216],"d\">":[171,217],"<mml:mi>c</mml:mi>":[183,229],"<mml:mo>+</mml:mo>":[188,231],"<mml:mi>d</mml:mi>":[189,232],"encoding=\"application/x-tex\">P(x,":[192,235],"y)":[193,236],"cy^2":[195],"+":[196,239],"d</mml:annotation>":[197,240],"cx":[238],"which":[245],"arise":[246],"when":[247],"looking":[248],"for":[249],"points":[251],"elliptic":[254],"curve":[255],"with":[256],"rational":[258],"2-torsion":[259],"point.":[260]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":5}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}