Lithuanian Mathematical Journal

, Volume 53, Issue 2, pp 143–148 | Cite as

Repdigit Keith numbers

Article
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Abstract

A Keith number is a positive integer N with the decimal representation a1a2ak such that k ≥ 2 and N appears in the sequence that starts with a1, a2,…, ak and for which each term afterwards is the sum of the k preceding terms. In 2007, Klazar and Luca [M. Klazar and F. Luca, Counting Keith numbers, J. Integer Seq., 10(2):Article 07.2.2, 2007] proved that there are only finitely many Keith numbers with only one distinct digit (so-called repdigits). In this paper, we prove that there are no Keith numbers which are repdigits.

Keywords

Keith number generalized Fibonacci recurrence repdigits 

MSC

11B39 11A63 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad del CaucaPopayánColombia
  2. 2.Centro de Ciencias MatemáticasUniversidad Nacional Autónoma de MéxicoMoreliaMexico
  3. 3.Fundación Marcos Moshinsky A.C., Instituto de Ciencias Nucleares de la UNAMMéxico D.F.Mexico
  4. 4.Instituto de MatemáticasUniversidad Nacional Autónoma de MéxicoMéxico D.F.Mexico

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