{"id":"https://openalex.org/W2063934242","doi":"https://doi.org/10.1090/s0025-5718-96-00687-4","title":"Simultaneous Pell equations","display_name":"Simultaneous Pell equations","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2063934242","doi":"https://doi.org/10.1090/s0025-5718-96-00687-4","mag":"2063934242"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-96-00687-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00687-4","pdf_url":"https://www.ams.org/mcom/1996-65-213/S0025-5718-96-00687-4/S0025-5718-96-00687-4.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/1996-65-213/S0025-5718-96-00687-4/S0025-5718-96-00687-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080997716","display_name":"W. S. Anglin","orcid":null},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"W. Anglin","raw_affiliation_strings":["Department of Mathematics and Statistics, McGill University, 805 Sherbrooke West, Montreal, Quebec, Canada H3A 2K6"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, McGill University, 805 Sherbrooke West, Montreal, Quebec, Canada H3A 2K6","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080997716"],"corresponding_institution_ids":["https://openalex.org/I5023651"],"apc_list":null,"apc_paid":null,"fwci":0.9789,"has_fulltext":true,"cited_by_count":29,"citation_normalized_percentile":{"value":0.74541477,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"65","issue":"213","first_page":"355","last_page":"359"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9965000152587891,"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":0.9965000152587891,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9824000000953674,"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/T13095","display_name":"Plant-based Medicinal Research","score":0.9624000191688538,"subfield":{"id":"https://openalex.org/subfields/3004","display_name":"Pharmacology"},"field":{"id":"https://openalex.org/fields/30","display_name":"Pharmacology, Toxicology and Pharmaceutics"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6285363435745239},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.5632669925689697},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.48541268706321716},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4450478255748749},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37068623304367065},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.36417537927627563},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.06461766362190247}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6285363435745239},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.5632669925689697},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.48541268706321716},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4450478255748749},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37068623304367065},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.36417537927627563},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.06461766362190247},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-96-00687-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00687-4","pdf_url":"https://www.ams.org/mcom/1996-65-213/S0025-5718-96-00687-4/S0025-5718-96-00687-4.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/s0025-5718-96-00687-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00687-4","pdf_url":"https://www.ams.org/mcom/1996-65-213/S0025-5718-96-00687-4/S0025-5718-96-00687-4.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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2063934242.pdf","grobid_xml":"https://content.openalex.org/works/W2063934242.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1575761830","https://openalex.org/W1592775214","https://openalex.org/W2057182494","https://openalex.org/W2123174602","https://openalex.org/W2297456208","https://openalex.org/W3175367423","https://openalex.org/W4237975607"],"related_works":["https://openalex.org/W1892467659","https://openalex.org/W1529400504","https://openalex.org/W2349865494","https://openalex.org/W2998403542","https://openalex.org/W2808586768","https://openalex.org/W2372553222","https://openalex.org/W3157620392","https://openalex.org/W2925832130","https://openalex.org/W2045715842","https://openalex.org/W2105880240"],"abstract_inverted_index":{"Let":[0],"<inline-formula":[1,15,32,190,204,226,264,284,305,379],"content-type=\"math/mathml\">":[2,16,33,61,191,205,227,265,285,306,380],"<mml:math":[3,17,34,62,192,206,228,266,286,307,381],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[4,18,35,63,193,207,229,267,287,308,382],"alttext=\"upper":[5,19,36,194,208,268,288,383],"R\">":[6,195],"<mml:semantics>":[7,21,41,101,196,210,237,272,292,316,390],"<mml:mi>R</mml:mi>":[8,43,138,197,274,392],"<mml:annotation":[9,23,47,177,198,212,249,278,298,328],"encoding=\"application/x-tex\">R</mml:annotation>":[10,199],"</mml:semantics>":[11,25,49,182,200,214,251,280,300,332],"</mml:math>":[12,26,50,183,201,215,252,281,301,333],"</inline-formula>":[13,27,51,202,216,253,282,302,334],"and":[14,203,283,344,359],"S\">":[20,40,209],"<mml:mi>S</mml:mi>":[22,45,161,211,294,394],"encoding=\"application/x-tex\">S</mml:annotation>":[24,213],"be":[28],"positive":[29],"integers":[30],"with":[31],"R":[37,73,269,384],"greater-than":[38,385],"upper":[39,72,88,386],"<mml:mrow>":[42,238,273,293,317,391],"<mml:mo>&gt;</mml:mo>":[44,393],"</mml:mrow>":[46,248,277,297,327],"encoding=\"application/x-tex\">R&gt;S</mml:annotation>":[48],".":[52,217],"We":[53],"shall":[54],"call":[55],"the":[56,223,352,376],"simultaneous":[57,186],"Diophantine":[58],"equations":[59,188],"<disp-formula":[60],"alttext=\"StartLayout":[64],"1st":[65,67],"Row":[66],"Column":[68,77,93],"x":[69],"squared":[70,75,86,91],"minus":[71,87],"y":[74,90],"2nd":[76],"a":[78,94,336,365],"m":[79,95],"p":[80,96],"semicolon":[81,97],"equals":[82,98,270,290],"1":[83,99,231,235],"comma":[84,232,234,311,313],"z":[85],"S":[89,289,387],"3rd":[92],"EndLayout\">":[100],"<mml:mtable":[102],"columnalign=\"right":[103],"left":[104,106,108,110,112],"right":[105,107,109,111,113],"left\"":[114],"rowspacing=\"3pt\"":[115],"columnspacing=\"0em":[116],"2em":[117,119,121,123,125],"0em":[118,120,122,124],"0em\"":[126],"side=\"left\"":[127],"displaystyle=\"true\">":[128],"<mml:mtr>":[129],"<mml:mtd>":[130,144,167],"<mml:msup>":[131,139,154,162],"<mml:mi>x</mml:mi>":[132],"<mml:mn>2</mml:mn>":[133,141,156,164],"</mml:msup>":[134,142,157,165],"<mml:mo>":[135,158,395],"\u2212":[136,159],"</mml:mo>":[137,160],"<mml:mi>y</mml:mi>":[140,163],"</mml:mtd>":[143,166,174],"<mml:mi>a</mml:mi>":[145,168],"<mml:mi>m</mml:mi>":[146,169],"<mml:mi>p</mml:mi>":[147,170],"<mml:mo>;</mml:mo>":[148,171],"<mml:mo>=</mml:mo>":[149,172,275,295],"<mml:mn>1</mml:mn>":[150,173,241,245],"<mml:mo>,</mml:mo>":[151,242,244,321,323],"<mml:mtext>":[152],"</mml:mtext>":[153],"<mml:mi>z</mml:mi>":[155],"</mml:mtr>":[175],"</mml:mtable>":[176],"encoding=\"application/x-tex\">\\begin{align*}":[178],"x^2-Ry^2&amp;=1,\\":[179],"z^2-Sy^2&amp;=1":[180],"\\end{align*}</mml:annotation>":[181],"</disp-formula>":[184],"<italic>":[185],"Pell":[187],"in":[189],"</italic>":[218],"Each":[219],"such":[220],"pair":[221],"has":[222],"trivial":[224],"solution":[225],"alttext=\"left-parenthesis":[230,309],"0":[233],"right-parenthesis\">":[236,315],"<mml:mo":[239,246,318,325],"stretchy=\"false\">(</mml:mo>":[240,319],"<mml:mn>0</mml:mn>":[243],"stretchy=\"false\">)</mml:mo>":[247,326],"encoding=\"application/x-tex\">(1,0,1)</mml:annotation>":[250],"but":[254],"some":[255],"pairs":[256],"have":[257],"nontrivial":[258],"solutions":[259,355,377],"too.":[260],"For":[261],"example,":[262],"if":[263],"11\">":[271],"<mml:mn>11</mml:mn>":[276],"encoding=\"application/x-tex\">R=11</mml:annotation>":[279],"56\">":[291],"<mml:mn>56</mml:mn>":[296],"encoding=\"application/x-tex\">S=56</mml:annotation>":[299],",":[303],"then":[304],"199":[310],"60":[312],"449":[314],"<mml:mn>199</mml:mn>":[320],"<mml:mn>60</mml:mn>":[322],"<mml:mn>449</mml:mn>":[324],"encoding=\"application/x-tex\">(199,":[329],"60,":[330],"449)</mml:annotation>":[331],"is":[335,347,356,361],"solution.":[337],"Using":[338],"theorems":[339],"due":[340],"to":[341,349,363],"Baker,":[342],"Davenport,":[343],"Waldschmidt,":[345],"it":[346,360],"possible":[348,362],"show":[350],"that":[351],"number":[353],"of":[354,368],"always":[357],"finite,":[358],"give":[364],"complete":[366],"list":[367],"them.":[369],"In":[370],"this":[371],"paper":[372],"we":[373],"report":[374],"on":[375],"when":[378],"less-than-or-equal-to":[388],"200\">":[389],"\u2264":[396]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}