Even perfect numbers in generalized Pell sequences

Abstract

In this paper, by using linear forms in logarithms and the Baker–Davenport reduction procedure we prove that there are no even perfect numbers appearing in generalized Pell sequences. We also deduce some interesting results involving generalized Pell numbers, which we believe are of independent interest. This paper continues a previous work that searched for perfect numbers in the classical Pell sequence.

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Correspondence to Jhon J. Bravo.

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The author was supported in part by Projects VRI ID 4689 (Universidad del Cauca) and Colciencias 110371250560.

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Bravo, J.J., Herrera, J.L. Even perfect numbers in generalized Pell sequences. Lith Math J (2020). https://doi.org/10.1007/s10986-020-09505-6

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MSC

  • 11B39
  • 11J86

Keywords

  • generalized Pell number
  • perfect number
  • linear form in logarithms
  • reduction method