{"id":"https://openalex.org/W4224304584","doi":"https://doi.org/10.3390/axioms11050184","title":"A New Solution to a Cubic Diophantine Equation","display_name":"A New Solution to a Cubic Diophantine Equation","publication_year":2022,"publication_date":"2022-04-19","ids":{"openalex":"https://openalex.org/W4224304584","doi":"https://doi.org/10.3390/axioms11050184"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11050184","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050184","pdf_url":"https://www.mdpi.com/2075-1680/11/5/184/pdf?version=1650361068","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/5/184/pdf?version=1650361068","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055631392","display_name":"J. C. Butcher","orcid":"https://orcid.org/0000-0001-6499-9851"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"John Butcher","raw_affiliation_strings":["Department of Mathematics, University of Auckland, Auckland 1010, New Zealand"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Auckland, Auckland 1010, New Zealand","institution_ids":["https://openalex.org/I154130895"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055631392"],"corresponding_institution_ids":["https://openalex.org/I154130895"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.5863,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.58266585,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"11","issue":"5","first_page":"184","last_page":"184"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9980999827384949,"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"}},"topics":[{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9980999827384949,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9965999722480774,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9922999739646912,"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/diophantine-equation","display_name":"Diophantine equation","score":0.9418966770172119},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7424523830413818},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.7107328176498413},{"id":"https://openalex.org/keywords/ramanujans-sum","display_name":"Ramanujan's sum","score":0.6207127571105957},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.5839838981628418},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5484526753425598},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.43942195177078247},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3393712043762207},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3214629292488098},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06985020637512207}],"concepts":[{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.9418966770172119},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7424523830413818},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.7107328176498413},{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.6207127571105957},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5839838981628418},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5484526753425598},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.43942195177078247},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3393712043762207},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3214629292488098},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06985020637512207},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11050184","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050184","pdf_url":"https://www.mdpi.com/2075-1680/11/5/184/pdf?version=1650361068","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:9c7971d2022d4722a531cc10a4479b2f","is_oa":true,"landing_page_url":"https://doaj.org/article/9c7971d2022d4722a531cc10a4479b2f","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 5, p 184 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/5/184/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11050184","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 11; Issue 5; Pages: 184","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11050184","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050184","pdf_url":"https://www.mdpi.com/2075-1680/11/5/184/pdf?version=1650361068","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4224304584.pdf","grobid_xml":"https://content.openalex.org/works/W4224304584.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2009983924","https://openalex.org/W2798191997","https://openalex.org/W6750761771"],"related_works":["https://openalex.org/W2025770640","https://openalex.org/W2029234250","https://openalex.org/W2379447811","https://openalex.org/W1553843799","https://openalex.org/W4298335810","https://openalex.org/W2462246956","https://openalex.org/W2351522589","https://openalex.org/W2387613912","https://openalex.org/W1755263897","https://openalex.org/W4313233328"],"abstract_inverted_index":{"A":[0],"positive":[1,12],"integer,":[2],"which":[3,30],"can":[4,68],"be":[5,69],"written":[6,70],"as":[7,20,35],"the":[8,36,45,57,60,77,94],"sum":[9],"of":[10,59,73,90],"two":[11,15,74],"cubes":[13],"in":[14,71,76],"different":[16],"ways,":[17],"is":[18,28,53,81],"known":[19],"a":[21],"\u201cRamanujan":[22],"number\u201d.":[23],"The":[24],"most":[25],"famous":[26],"example":[27],"1729=103+93=123+13,":[29],"was":[31],"identified":[32],"by":[33],"Ramanujan":[34],"lowest":[37],"such":[38],"number.":[39],"In":[40],"this":[41],"paper,":[42],"we":[43],"consider":[44],"homogeneous":[46],"cubic":[47],"Diophantine":[48],"equation":[49],"x3+y3=u3+v3,":[50],"where":[51],"there":[52],"no":[54],"restriction":[55],"on":[56],"signs":[58],"integers":[61],"x,y,u,v.":[62],"We":[63],"show":[64],"that":[65,84],"every":[66],"solution":[67],"terms":[72],"parameters":[75],"ring":[78],"Z\u22123.":[79],"It":[80],"also":[82],"shown":[83],"solutions":[85],"with":[86],"arbitrarily":[87],"high":[88],"values":[89],"max(|x|,|y|,|u|,|v|)":[91],"arise":[92],"amongst":[93],"primitive":[95],"solutions.":[96]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
