{"id":"https://openalex.org/W2082811707","doi":"https://doi.org/10.1090/s0025-5718-97-00830-2","title":"On searching for solutions of the Diophantine equation \ud835\udc65\u00b3+\ud835\udc66\u00b3+\ud835\udc67\u00b3=\ud835\udc5b","display_name":"On searching for solutions of the Diophantine equation \ud835\udc65\u00b3+\ud835\udc66\u00b3+\ud835\udc67\u00b3=\ud835\udc5b","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W2082811707","doi":"https://doi.org/10.1090/s0025-5718-97-00830-2","mag":"2082811707"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-97-00830-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-97-00830-2","pdf_url":"https://www.ams.org/mcom/1997-66-218/S0025-5718-97-00830-2/S0025-5718-97-00830-2.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/1997-66-218/S0025-5718-97-00830-2/S0025-5718-97-00830-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010911834","display_name":"Kenji Koyama","orcid":"https://orcid.org/0000-0002-1467-7050"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kenji Koyama","raw_affiliation_strings":["NTT Communication Science Laboratories 2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-02 Japan","NTT Communication Science Laboratories, 2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-02, Japan#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NTT Communication Science Laboratories 2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-02 Japan","institution_ids":[]},{"raw_affiliation_string":"NTT Communication Science Laboratories, 2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-02, Japan#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024082073","display_name":"Yukio Tsuruoka","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yukio Tsuruoka","raw_affiliation_strings":["NTT Communication Science Laboratories 2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-02 Japan","NTT Communication Science Laboratories, 2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-02, Japan#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NTT Communication Science Laboratories 2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-02 Japan","institution_ids":[]},{"raw_affiliation_string":"NTT Communication Science Laboratories, 2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-02, Japan#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021311433","display_name":"Hiroshi Sekigawa","orcid":"https://orcid.org/0009-0003-1770-0994"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hiroshi Sekigawa","raw_affiliation_strings":["NTT Communication Science Laboratories 2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-02 Japan","NTT Communication Science Laboratories, 2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-02, Japan#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NTT Communication Science Laboratories 2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-02 Japan","institution_ids":[]},{"raw_affiliation_string":"NTT Communication Science Laboratories, 2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-02, Japan#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7833,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.83957021,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"66","issue":"218","first_page":"841","last_page":"851"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9814000129699707,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9814000129699707,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9244999885559082,"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/algorithm","display_name":"Algorithm","score":0.6277321577072144},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3787700831890106},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.35975855588912964}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6277321577072144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3787700831890106},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35975855588912964}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-97-00830-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-97-00830-2","pdf_url":"https://www.ams.org/mcom/1997-66-218/S0025-5718-97-00830-2/S0025-5718-97-00830-2.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/s0025-5718-97-00830-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-97-00830-2","pdf_url":"https://www.ams.org/mcom/1997-66-218/S0025-5718-97-00830-2/S0025-5718-97-00830-2.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/W2082811707.pdf","grobid_xml":"https://content.openalex.org/works/W2082811707.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W46055081","https://openalex.org/W125579651","https://openalex.org/W181258777","https://openalex.org/W1535499733","https://openalex.org/W1542127628","https://openalex.org/W1553318827","https://openalex.org/W1555475515","https://openalex.org/W1966625227","https://openalex.org/W2000683955","https://openalex.org/W2025857263","https://openalex.org/W2039132442","https://openalex.org/W2042814246","https://openalex.org/W2061465666","https://openalex.org/W2335584542","https://openalex.org/W2556959701","https://openalex.org/W2594541846","https://openalex.org/W2798483379","https://openalex.org/W4248458881","https://openalex.org/W4299857944"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W2350741829"],"abstract_inverted_index":{"We":[0,295],"propose":[1],"a":[2,49,231,297],"new":[3,284],"search":[4,299],"algorithm":[5,171,285],"to":[6],"solve":[7],"the":[8,283],"equation":[9,233],"<inline-formula":[10,53,74,103,173,200,238,304,319],"content-type=\"math/mathml\">":[11,54,75,104,174,201,239,305,320],"<mml:math":[12,55,76,105,175,202,240,306,321],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[13,56,77,106,176,203,241,307,322],"alttext=\"x":[14],"cubed":[15,18,21,245],"plus":[16,19],"y":[17,113,178],"z":[20,117,205],"equals":[22],"n\">":[23,247],"<mml:semantics>":[24,60,82,120,180,207,248,309,331],"<mml:mrow>":[25,61,83,121,181,208,249,332],"<mml:msup>":[26,31,36,256],"<mml:mi>x</mml:mi>":[27,89,129,255],"<mml:mn>3</mml:mn>":[28,33,38,262],"</mml:msup>":[29,34,39,263],"<mml:mo>+</mml:mo>":[30,35],"<mml:mi>y</mml:mi>":[32,141,187],"<mml:mi>z</mml:mi>":[37,153,214],"<mml:mo>=</mml:mo>":[40,95],"<mml:mi>n</mml:mi>":[41,62,267,310,333],"</mml:mrow>":[42,65,88,94,96,128,134,140,146,152,158,161,186,192,193,213,219,220,254,261,268],"<mml:annotation":[43,66,97,162,194,221,269,311],"encoding=\"application/x-tex\">x^3+y^3+z^3=n</mml:annotation>":[44],"</mml:semantics>":[45,68,99,166,196,223,273,313],"</mml:math>":[46,69,100,167,197,224,274,314],"</inline-formula>":[47,70,101,168,198,225,275,315],"for":[48,300],"fixed":[50],"value":[51],"of":[52,237,303],"alttext=\"n":[57,323],"greater-than":[58],"0\">":[59],"<mml:mo>&gt;</mml:mo>":[63],"<mml:mn>0</mml:mn>":[64],"encoding=\"application/x-tex\">n&gt;0</mml:annotation>":[67],".":[71,276],"By":[72,277],"parametrizing":[73],"alttext=\"StartAbsoluteValue":[78,177,204,242],"x":[79,109,243],"EndAbsoluteValue":[80,110,114,118,244],"equals\">":[81],"<mml:mrow":[84,90,124,130,136,142,148,154,182,188,209,215,250,257],"class=\"MJX-TeXAtom-ORD\">":[85,91,125,131,137,143,149,155,183,189,210,216,251,258],"<mml:mo":[86,92,122,126,132,138,144,150,156,159,184,190,211,217,252,259,341,348],"stretchy=\"false\">|</mml:mo>":[87,93,127,133,139,145,151,157,185,191,212,218,253,260],"encoding=\"application/x-tex\">|x|=</mml:annotation>":[98],"min":[102],"alttext=\"left-parenthesis":[107],"StartAbsoluteValue":[108,112,116],"comma":[111,115],"right-parenthesis\">":[119,330],"stretchy=\"false\">(</mml:mo>":[123,342],"<mml:mo>,</mml:mo>":[135,147],"stretchy=\"false\">)</mml:mo>":[160,349],"encoding=\"application/x-tex\">(|x|,":[163],"|y|,":[164],"|z|)</mml:annotation>":[165],",":[169],"this":[170],"obtains":[172],"EndAbsoluteValue\">":[179,206],"encoding=\"application/x-tex\">|y|</mml:annotation>":[195],"and":[199],"encoding=\"application/x-tex\">|z|</mml:annotation>":[222],"(if":[226],"they":[227],"exist)":[228],"by":[229],"solving":[230],"quadratic":[232],"derived":[234],"from":[235],"divisors":[236],"plus-or-minus":[246,325],"<mml:mo>":[264,334,337,344],"\u00b1":[265,338],"</mml:mo>":[266,336,339,346],"encoding=\"application/x-tex\">|x|^3":[270],"\\pm":[271],"n</mml:annotation>":[272],"using":[278],"several":[279],"efficient":[280],"number-theoretic":[281],"sieves,":[282],"is":[286],"much":[287],"faster":[288],"on":[289],"average":[290],"than":[291],"previous":[292],"straightforward":[293],"algorithms.":[294],"performed":[296],"computer":[298],"51":[301],"values":[302],"alttext=\"n\">":[308],"encoding=\"application/x-tex\">n</mml:annotation>":[312],"below":[316],"1000":[317],"(except":[318],"identical-to":[324],"4":[326],"left-parenthesis":[327],"mod":[328],"9":[329],"\u2261":[335],"<mml:mn>4</mml:mn>":[340],"<mml:mi>mod</mml:mi>":[343],"\u2061":[345],"<mml:mn>9</mml:mn>":[347],"</":[350]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}