Repdigits as sums of four Pell numbers

  • Florian Luca
  • Benedict Vasco Normenyo
  • Alain Togbé
Original Article


In this paper, all base 10 repdigits expressible as sums of four Pell numbers are found.


Pell numbers Rep-digit Linear forms in complex and p-adic logarithms 

Mathematics Subject Classification

11A25 11B39 11J86 



F. L. was supported in part by grant CPRR160325161141 and an A-rated scientist award both from the NRF of South Africa, the Focus Area: Number Theory grant from CoEMaSS, Wits, and by grant no. 17-02804S of the Czech Granting Agency. The authors would like to thank the referee for the valuable comments to improve the manuscript.


  1. 1.
    Bugeaud, Y., Mignotte, M., Siksek, S.: Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers. Ann. Math. 2(163), 969–1018 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Dujella, A., Pethő, A.: A generalization of a theorem of Baker and Davenport. Q. J. Math. 49(2), 291–306 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Luca, F.: Repdigits as sums of three Fibonacci numbers. Math. Commun. 17, 1–11 (2012)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Matveev, E.M.: An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers, II. Izv. Ross. Akad. Nauk Ser. Mat. 64, 125–180 (2000). (English transl Izv. Math. 64 (2000), 1217–1269)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Normenyo, B.V., Luca, F., Togbé, A.: Repdigits as sums of three Pell numbers, To appear in Periodica Mathematica HungaricaGoogle Scholar
  6. 6.
    de Weger, B.M.M.: Algorithms for diophantine equations. CWI Tract, 65. Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam (1989)Google Scholar

Copyright information

© Sociedad Matemática Mexicana 2018

Authors and Affiliations

  1. 1.Institut de Mathématiques et de Sciences PhysiquesDangboBénin
  2. 2.School of MathematicsUniversity of the WitwatersrandWitsSouth Africa
  3. 3.Department of Mathematics, Faculty of SciencesUniversity of OstravaOstrava 1Czech Republic
  4. 4.Department of Mathematics, Statistics and Computer SciencePurdue University NorthwestWestvilleUSA

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