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Pell or Pell–Lucas numbers as concatenations of two repdigits in base b

  • Kouèssi Norbert Adédji,
  • Alan Filipin,
  • Salah Eddine Rihane,
  • Alain Togbé

摘要

Let b be a positive integer such that \(b\ge 2\) b 2 . In this study, we prove that for a fixed b,  there exists only a finite Pell and Pell–Lucas numbers as concatenations of two repdigits in base b. As a corollary, we show that the largest Pell or Pell–Lucas numbers which can be expressible as concatenations of two distinct repdigits in base b with \(2\le b\le 10\) 2 b 10 are \(P_{11} = 5741\) P 11 = 5741 and \(Q_{5}=82,\) Q 5 = 82 , respectively.