{"title":"On Padovan or Perrin numbers as products of three repdigits in base $$\\delta $$","authors":"Pagdame Tiebekabe, Kouèssi Norbert Adédji","doi":"10.1007/s13226-024-00599-z","DOIUrl":null,"url":null,"abstract":"<p>Let <span>\\(P_m\\)</span> and <span>\\(E_m\\)</span> be the <i>m</i>-th Padovan and Perrin numbers, respectively. In this paper, we prove that for a fixed integer <span>\\(\\delta \\)</span> with <span>\\(\\delta \\ge 2\\)</span> there exists finitely many Padovan and Perrin numbers that can be represented as products of three repdigits in base <span>\\(\\delta .\\)</span> Moreover, we explicitly find these numbers for <span>\\(2\\le \\delta \\le 10\\)</span> as an application.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"48 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indian Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13226-024-00599-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Let \(P_m\) and \(E_m\) be the m-th Padovan and Perrin numbers, respectively. In this paper, we prove that for a fixed integer \(\delta \) with \(\delta \ge 2\) there exists finitely many Padovan and Perrin numbers that can be represented as products of three repdigits in base \(\delta .\) Moreover, we explicitly find these numbers for \(2\le \delta \le 10\) as an application.
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