Perfect fibonacci and lucas numbers

  • Florian Luca


In this note, we show that the classical Fibonacci and Lucas sequence do not contain any perfect number.

1991 AMS Mathematics Subject Classification

11A25 11B39 


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  1. [1]
    Cohn J.H.E.,Square Fibonacci numbers, etc., Fibo. Quart.,2 (1964).Google Scholar
  2. [2]
    Dickson L.E.,History of the Theory of Numbers, Vol. I, Divisiblity and Primality, Chelsea Publishing Company, New York, 1966.zbMATHGoogle Scholar
  3. [3]
    Luca F.,Euler Indicators of Lucas Sequences, Bull. Math. Soc. Sc. Mat. Roumanie, Tome40 (88) (1997), 151–163.zbMATHGoogle Scholar
  4. [4]
    Luca F.,Arithmetic functions of Fibonacci and Lucas numbers, Fibo. Quart.,37 (1999), 265–268.zbMATHMathSciNetGoogle Scholar
  5. [5]
    Ribenboim P.,Square Classes of Fibonacci and Lucas numbers, Portugaliae Math.46 (1) (1989), 159–176.zbMATHMathSciNetGoogle Scholar
  6. [6]
    Robbins N.,On Fibonacci numbers of the form px 2 where p is a prime, Fibo. Quart.21 (1983), 266–271.zbMATHMathSciNetGoogle Scholar
  7. [7]
    Rosen K.H.,Elementary number theory and its applications, Addison-Wesley, 1984.Google Scholar

Copyright information

© Springer 2000

Authors and Affiliations

  1. 1.Mathematical InstituteCzech Academy of SciencesPraha 1Czech Republic

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