Ana Cecilia García-Lomelí, Santos Hernández-Hernández
{"title":"形式为6a±6b±6c的多瓦数","authors":"Ana Cecilia García-Lomelí, Santos Hernández-Hernández","doi":"10.18273/revint.v41n2-2023001","DOIUrl":null,"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":0.0000,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":null,\"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\":0.0000,\"publicationDate\":\"2023-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista Integracion\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.18273/revint.v41n2-2023001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Integracion","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18273/revint.v41n2-2023001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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.
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