Ana Cecilia García-Lomelí, Santos Hernández-Hernández
{"title":"The Padovan numbers of the form 6a ± 6b ± 6c","authors":"Ana Cecilia García-Lomelí, Santos Hernández-Hernández","doi":"10.18273/revint.v41n2-2023001","DOIUrl":"https://doi.org/10.18273/revint.v41n2-2023001","url":null,"abstract":"Let (Pn)n>0 be the Padovan sequence given by P0 = 0, P1 = P2 = 1 and the recurrence formula Pn+3 = Pn+1 + Pn for all n > 0. In this note, we completely solve the Diophantine equation Pn = 6a ± 6b ± 6c in non-negative integers (n, a, b, c) with a > b > c > 0.","PeriodicalId":30593,"journal":{"name":"Revista Integracion","volume":"200 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135203939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}