{"id":"https://openalex.org/W2041725848","doi":"https://doi.org/10.1090/s0025-5718-96-00768-5","title":"Equal sums of four seventh powers","display_name":"Equal sums of four seventh powers","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2041725848","doi":"https://doi.org/10.1090/s0025-5718-96-00768-5","mag":"2041725848"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-96-00768-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00768-5","pdf_url":"https://www.ams.org/mcom/1996-65-216/S0025-5718-96-00768-5/S0025-5718-96-00768-5.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/1996-65-216/S0025-5718-96-00768-5/S0025-5718-96-00768-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067274100","display_name":"Randy L. Ekl","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Randy Ekl","raw_affiliation_strings":["930 Lancaster Lane, Lake Zurich, Illinois 60047"],"affiliations":[{"raw_affiliation_string":"930 Lancaster Lane, Lake Zurich, Illinois 60047","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067274100"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5338,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.79910714,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"65","issue":"216","first_page":"1755","last_page":"1756"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9998999834060669,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9998999834060669,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9986000061035156,"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/T12504","display_name":"Mathematics and Applications","score":0.9973999857902527,"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/mathematics","display_name":"Mathematics","score":0.7994638681411743},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6780601143836975},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.5408412218093872},{"id":"https://openalex.org/keywords/workstation","display_name":"Workstation","score":0.5018877983093262},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3839128613471985},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3395459055900574},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13074329495429993},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.059280723333358765}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7994638681411743},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6780601143836975},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.5408412218093872},{"id":"https://openalex.org/C67953723","wikidata":"https://www.wikidata.org/wiki/Q192525","display_name":"Workstation","level":2,"score":0.5018877983093262},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3839128613471985},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3395459055900574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13074329495429993},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.059280723333358765},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-96-00768-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00768-5","pdf_url":"https://www.ams.org/mcom/1996-65-216/S0025-5718-96-00768-5/S0025-5718-96-00768-5.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:10.1.1.192.144","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.144","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/1996-65-216/S0025-5718-96-00768-5/S0025-5718-96-00768-5.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.95.8485","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.95.8485","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/1996-65-216/S0025-5718-96-00768-5/S0025-5718-96-00768-5.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-96-00768-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00768-5","pdf_url":"https://www.ams.org/mcom/1996-65-216/S0025-5718-96-00768-5/S0025-5718-96-00768-5.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/W2041725848.pdf","grobid_xml":"https://content.openalex.org/works/W2041725848.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1555475515","https://openalex.org/W1694128183","https://openalex.org/W2004822353","https://openalex.org/W2112747630","https://openalex.org/W2593170163","https://openalex.org/W3175367423","https://openalex.org/W4256472979","https://openalex.org/W4388288416"],"related_works":["https://openalex.org/W2045348955","https://openalex.org/W2352028719","https://openalex.org/W2584886384","https://openalex.org/W2378667902","https://openalex.org/W2052769075","https://openalex.org/W2791088446","https://openalex.org/W4206808270","https://openalex.org/W2134078163","https://openalex.org/W88892441","https://openalex.org/W157202813"],"abstract_inverted_index":{"In":[0],"this":[1,221],"paper,":[2],"the":[3,8,232],"method":[4],"used":[5],"to":[6],"find":[7],"smallest,":[9],"nontrivial,":[10],"positive":[11],"integer":[12],"solution":[13,123],"of":[14,235],"<inline-formula":[15],"content-type=\"math/mathml\">":[16,126],"<mml:math":[17,127],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[18,128],"alttext=\"a":[19],"1":[20,44],"Superscript":[21,27,33,39,45,51,57,63,130,135,140,145,150,155,160,165],"7":[22,28,34,40,46,52,58,131,136,141,146,151,156,161,166],"Baseline":[23,29,35,41,47,53,59,132,137,142,147,152,157,162,167],"plus":[24,30,36,48,54,60,133,138,143,153,158,163],"a":[25,31,37],"2":[26,50],"3":[32,56],"4":[38,62],"equals":[42,148],"b":[43,49,55,61],"7\">":[64],"<mml:semantics>":[65,169],"<mml:mrow>":[66,170],"<mml:msubsup>":[67,73,79,85,91,97,103,109],"<mml:mi>a</mml:mi>":[68,74,80,86],"<mml:mn>1</mml:mn>":[69,93],"<mml:mn>7</mml:mn>":[70,76,82,88,94,100,106,112,173,178,183,188,193,198,203,208],"</mml:msubsup>":[71,77,83,89,95,101,107,113],"<mml:mo>+</mml:mo>":[72,78,84,96,102,108,175,180,185,195,200,205],"<mml:mn>2</mml:mn>":[75,99],"<mml:mn>3</mml:mn>":[81,105],"<mml:mn>4</mml:mn>":[87,111],"<mml:mo>=</mml:mo>":[90,190],"<mml:mi>b</mml:mi>":[92,98,104,110],"</mml:mrow>":[114,211],"<mml:annotation":[115,212],"encoding=\"application/x-tex\">a_1^7+a_2^7+a_3^7+a_4^7=b_1^7+b_2^7+b_3^7+b_4^7</mml:annotation>":[116],"</mml:semantics>":[117,216],"</mml:math>":[118,217],"</inline-formula>":[119],"is":[120,124],"discussed.":[121],"The":[122],"<disp-formula":[125],"alttext=\"149":[129],"123":[134],"14":[139],"10":[144],"146":[149],"129":[154],"90":[159],"15":[164],"period\">":[168],"<mml:msup>":[171,176,181,186,191,196,201,206],"<mml:mn>149</mml:mn>":[172],"</mml:msup>":[174,179,184,189,194,199,204,209],"<mml:mn>123</mml:mn>":[177],"<mml:mn>14</mml:mn>":[182],"<mml:mn>10</mml:mn>":[187],"<mml:mn>146</mml:mn>":[192],"<mml:mn>129</mml:mn>":[197],"<mml:mn>90</mml:mn>":[202],"<mml:mn>15</mml:mn>":[207],"<mml:mo>.</mml:mo>":[210],"encoding=\"application/x-tex\">\\begin{equation*}":[213],"149^7+123^7+14^7+10^7=":[214],"146^7+129^7+90^7+15^7.\\end{equation*}</mml:annotation>":[215],"</disp-formula>":[218],"Factors":[219],"enabling":[220],"discovery":[222],"are":[223],"advances":[224],"in":[225],"computing":[226],"power,":[227],"available":[228],"workstation":[229],"memory,":[230],"and":[231],"appropriate":[233],"choice":[234],"optimized":[236],"algorithms.":[237]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}