{"id":"https://openalex.org/W2082542085","doi":"https://doi.org/10.1090/s0025-5718-99-01071-6","title":"On sums of seven cubes","display_name":"On sums of seven cubes","publication_year":1999,"publication_date":"1999-02-11","ids":{"openalex":"https://openalex.org/W2082542085","doi":"https://doi.org/10.1090/s0025-5718-99-01071-6","mag":"2082542085"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-99-01071-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01071-6","pdf_url":"https://www.ams.org/mcom/1999-68-227/S0025-5718-99-01071-6/S0025-5718-99-01071-6.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/1999-68-227/S0025-5718-99-01071-6/S0025-5718-99-01071-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025064332","display_name":"Fran\u00e7ois Bertault","orcid":null},"institutions":[{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"F. Bertault","raw_affiliation_strings":["D\u00c3\u00a9partement de math\u00c3\u00a9matiques, Universit\u00c3\u00a9 de Lille I, 59 655 Villeneuve d\u00e2\u0080\u0099Ascq, France","D\u00e9partement de math\u00e9matiques, Universit\u00e9 de Lille I, 59 655 Villeneuve d\u2019Ascq, France"],"affiliations":[{"raw_affiliation_string":"D\u00c3\u00a9partement de math\u00c3\u00a9matiques, Universit\u00c3\u00a9 de Lille I, 59 655 Villeneuve d\u00e2\u0080\u0099Ascq, France","institution_ids":[]},{"raw_affiliation_string":"D\u00e9partement de math\u00e9matiques, Universit\u00e9 de Lille I, 59 655 Villeneuve d\u2019Ascq, France","institution_ids":["https://openalex.org/I2279609970"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090497983","display_name":"Olivier Ramar\u00e9","orcid":"https://orcid.org/0000-0002-8765-0465"},"institutions":[{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4210127166","display_name":"Centre Inria de l'Universit\u00e9 de Lorraine","ror":"https://ror.org/03fcjvn64","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210127166"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"O. Ramar\u00e9","raw_affiliation_strings":["LORIA, BP 101, 54600 Villers-l\u00e8s-Nancy Cedex, France"],"affiliations":[{"raw_affiliation_string":"LORIA, BP 101, 54600 Villers-l\u00e8s-Nancy Cedex, France","institution_ids":["https://openalex.org/I4210127166","https://openalex.org/I4210121838"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108687700","display_name":"Peter Zimmermann","orcid":null},"institutions":[{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4210127166","display_name":"Centre Inria de l'Universit\u00e9 de Lorraine","ror":"https://ror.org/03fcjvn64","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210127166"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"P. Zimmermann","raw_affiliation_strings":["Dpartement de mathmatiques, Universit de Lille I, 59 655 Villeneuve d'Ascq, France","LORIA, BP 101, 54600 Villers-ls-Nancy Cedex, France","Polynomials, Combinatorics, Arithmetic"],"affiliations":[{"raw_affiliation_string":"Dpartement de mathmatiques, Universit de Lille I, 59 655 Villeneuve d'Ascq, France","institution_ids":["https://openalex.org/I2279609970"]},{"raw_affiliation_string":"LORIA, BP 101, 54600 Villers-ls-Nancy Cedex, France","institution_ids":["https://openalex.org/I4210127166","https://openalex.org/I4210121838"]},{"raw_affiliation_string":"Polynomials, Combinatorics, Arithmetic","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025064332"],"corresponding_institution_ids":["https://openalex.org/I2279609970"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.15018855,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"68","issue":"227","first_page":"1303","last_page":"1310"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9993000030517578,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.6820571422576904},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.5272093415260315},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5158280730247498},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45867663621902466},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.42077669501304626},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3104085326194763},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2993107736110687},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10366764664649963}],"concepts":[{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.6820571422576904},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.5272093415260315},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5158280730247498},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45867663621902466},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.42077669501304626},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3104085326194763},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2993107736110687},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10366764664649963},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-99-01071-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01071-6","pdf_url":"https://www.ams.org/mcom/1999-68-227/S0025-5718-99-01071-6/S0025-5718-99-01071-6.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:10.1.1.296.5539","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.296.5539","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/1999-68-227/S0025-5718-99-01071-6/S0025-5718-99-01071-6.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.304.9987","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.304.9987","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/1999-68-227/S0025-5718-99-01071-6/S0025-5718-99-01071-6.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:inria-00108056v1","is_oa":false,"landing_page_url":"https://inria.hal.science/inria-00108056","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation, 1999, 68 (227), pp.1303-1310","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-99-01071-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01071-6","pdf_url":"https://www.ams.org/mcom/1999-68-227/S0025-5718-99-01071-6/S0025-5718-99-01071-6.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/W2082542085.pdf","grobid_xml":"https://content.openalex.org/works/W2082542085.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W594222459","https://openalex.org/W1500096885","https://openalex.org/W1585160083","https://openalex.org/W1978516800","https://openalex.org/W1979700707","https://openalex.org/W2013065865","https://openalex.org/W2022898708","https://openalex.org/W2027404584","https://openalex.org/W2041041338","https://openalex.org/W2053518357","https://openalex.org/W2068534877","https://openalex.org/W2085924910","https://openalex.org/W2092182987","https://openalex.org/W2094144731","https://openalex.org/W2269232330","https://openalex.org/W3049545071","https://openalex.org/W4247458300"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2117548279","https://openalex.org/W2097470475","https://openalex.org/W2070252991","https://openalex.org/W2807449856","https://openalex.org/W4251428025","https://openalex.org/W2941201715","https://openalex.org/W2025727968","https://openalex.org/W4297742300","https://openalex.org/W4394650166"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,46],"every":[3,47],"integer":[4,48],"between":[5],"1290741":[6],"and":[7,56],"<inline-formula":[8],"content-type=\"math/mathml\">":[9],"<mml:math":[10],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[11],"alttext=\"3.375":[12],"times":[13],"10":[14],"Superscript":[15],"12\">":[16],"<mml:semantics>":[17],"<mml:mrow>":[18],"<mml:mn>3.375</mml:mn>":[19],"<mml:mo>\u00d7</mml:mo>":[20],"<mml:msup>":[21],"<mml:mn>10</mml:mn>":[22],"<mml:mrow":[23],"class=\"MJX-TeXAtom-ORD\">":[24],"<mml:mn>12</mml:mn>":[25],"</mml:mrow>":[26,28],"</mml:msup>":[27],"<mml:annotation":[29],"encoding=\"application/x-tex\">3.375\\times":[30],"10^{12}</mml:annotation>":[31],"</mml:semantics>":[32],"</mml:math>":[33],"</inline-formula>":[34],"is":[35,50,63],"a":[36,51,64],"sum":[37,65],"of":[38,66],"5":[39],"nonnegative":[40,68],"cubes,":[41],"from":[42],"which":[43,49],"we":[44],"deduce":[45],"cubic":[52,59],"residue":[53,60],"modulo":[54,61],"9":[55],"an":[57],"invertible":[58],"37":[62],"7":[67],"cubes.":[69]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}