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<p>Let <i>b</i> be an integer such that <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_758_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(b\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>b</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. In this paper, we investigate on Mulatu and generalized Lucas numbers which are products of four repdigits in base <i>b</i>. Further on, we will fully determine these numbers for any <i>b</i> between 2 and 12 for Mulatu numbers and special cases of Lucas numbers namely Fibonacci, Pell and balancing as an application. As a corollary, we will discuss on intersection of Mulatu and generalized Lucas numbers. The proofs are based on Baker’s theory on linear forms in logarithms of algebraic numbers and also the reduction method due to Bravo, Gómez and Luca.</p>

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On Mulatu and generalized Lucas numbers which are products of four b-repdigits with a consequence

  • 期刊论文

  • 发表日期：

    2025年2月10日

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  • Kouèssi Norbert Adédji

摘要

Let b be an integer such that \(b\ge 2\) b ≥ 2 . In this paper, we investigate on Mulatu and generalized Lucas numbers which are products of four repdigits in base b. Further on, we will fully determine these numbers for any b between 2 and 12 for Mulatu numbers and special cases of Lucas numbers namely Fibonacci, Pell and balancing as an application. As a corollary, we will discuss on intersection of Mulatu and generalized Lucas numbers. The proofs are based on Baker’s theory on linear forms in logarithms of algebraic numbers and also the reduction method due to Bravo, Gómez and Luca.