{"id":"https://openalex.org/W7221158049","doi":"https://doi.org/10.48550/arxiv.2610.12291","title":"Two Primes and Five Mixed Fibonacci-Lucas Summands","display_name":"Two Primes and Five Mixed Fibonacci-Lucas Summands","publication_year":2026,"publication_date":"2026-10-08","ids":{"openalex":"https://openalex.org/W7221158049","doi":"https://doi.org/10.48550/arxiv.2610.12291"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.12291","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.12291","pdf_url":"https://arxiv.org/pdf/2610.12291","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.12291","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5149321091","display_name":"Zhao Shen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shen, Zhao","raw_affiliation_strings":["School of Mathematics and Statistics , Central South University Changsha , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Central South University Changsha , China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5158018573","display_name":"Chenghe Xu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu, Chenghe","raw_affiliation_strings":["School of Mathematics and Statistics , Central South University Changsha , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Central South University Changsha , China","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I139660479"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9970999956130981,"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":0.9970999956130981,"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":0.0010999999940395355,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/sums-of-primes","display_name":"sums of primes","score":0.6690000295639038},{"id":"https://openalex.org/keywords/fibonacci-sequence","display_name":"Fibonacci numbers","score":0.9760000109672546},{"id":"https://openalex.org/keywords/lucas-numbers","display_name":"Lucas numbers","score":1.0},{"id":"https://openalex.org/keywords/circle-method","display_name":"circle method","score":0.7599999904632568}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.800599992275238},{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.7271000146865845},{"id":"https://openalex.org/C3634175","wikidata":"https://www.wikidata.org/wiki/Q2503280","display_name":"Lucas number","level":3,"score":0.6414999961853027},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5870000123977661},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5685999989509583},{"id":"https://openalex.org/C154977054","wikidata":"https://www.wikidata.org/wiki/Q1759646","display_name":"Lucas sequence","level":5,"score":0.4779999852180481},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40380001068115234},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.36239999532699585},{"id":"https://openalex.org/C79117305","wikidata":"https://www.wikidata.org/wiki/Q974295","display_name":"Fibonacci polynomials","level":4,"score":0.35929998755455017},{"id":"https://openalex.org/C174757984","wikidata":"https://www.wikidata.org/wiki/Q4351325","display_name":"Pisano period","level":5,"score":0.337799996137619},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.29100000858306885},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2768999934196472},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.25589999556541443},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.12291","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.12291","pdf_url":"https://arxiv.org/pdf/2610.12291","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.12291","doi":"https://doi.org/10.48550/arxiv.2610.12291","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.12291","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.12291","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.12291","pdf_url":"https://arxiv.org/pdf/2610.12291","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221158049.pdf","grobid_xml":"https://content.openalex.org/works/W7221158049.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1480319329","https://openalex.org/W1999118101","https://openalex.org/W2067837357","https://openalex.org/W2261238570","https://openalex.org/W2312841439","https://openalex.org/W2963524801","https://openalex.org/W3045462822","https://openalex.org/W4379793370","https://openalex.org/W4386842865","https://openalex.org/W4402831515","https://openalex.org/W4402901546","https://openalex.org/W6929425420","https://openalex.org/W7161692677","https://openalex.org/W7203661647","https://openalex.org/W7203888522"],"related_works":["https://openalex.org/W7203888522","https://openalex.org/W1679447045","https://openalex.org/W4295093715","https://openalex.org/W2088573002","https://openalex.org/W2014639792","https://openalex.org/W4403205917","https://openalex.org/W3130647434","https://openalex.org/W2215806274","https://openalex.org/W7097683033","https://openalex.org/W4407534257"],"abstract_inverted_index":{"Using":[0],"the":[1],"circle":[2],"method,":[3],"we":[4],"prove":[5],"that":[6],"every":[7],"sufficiently":[8],"large":[9],"positive":[10],"integer":[11],"is":[12],"a":[13],"sum":[14],"of":[15],"two":[16],"primes,":[17],"$u$":[18],"Fibonacci":[19],"numbers":[20,24],"and":[21,33],"$5-u$":[22],"Lucas":[23],"for":[25],"each":[26],"$u\\in\\{1,2,3,4\\}$.":[27],"All":[28],"recurrence":[29],"indices":[30],"are":[31],"positive,":[32],"terms":[34],"may":[35],"be":[36],"repeated.":[37]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-10T00:00:00"}
