Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 56: Issue 4
Perfect Pell and Pell–Lucas numbers
Authors: Jhon J. Bravo 1 and Florian Luca 2
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  • 1 Universidad del Cauca, Calle 5 No 4–70 Popayán, Colombia
  • 2 University of the Witwatersrand, Private Bag X3, Wits 2050, South Africa
DOI:
https://doi.org/10.1556/012.2019.56.4.1440
Page Count:
381–387
Publication Date:
01 Dec 2019
Online Publication Date:
Dec 2019
Article Category:
Research Article
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Abstract

The Pell sequence (Pn)n=0∞ is given by the recurrence Pn = 2Pn−1 + Pn−2 with initial condition P0 = 0, P1 = 1 and its associated Pell-Lucas sequence (Qn)n=0∞ is given by the same recurrence relation but with initial condition Q0 = 2, Q1 = 2. Here we show that 6 is the only perfect number appearing in these sequences. This paper continues a previous work that searched for perfect numbers in the Fibonacci and Lucas sequences.

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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896
Keywords:
Primary 11B39, 11A25; Perfect numbers; Recurrence sequences; Pell sequences; Pell–Lucas sequences

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