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

2022/10/18 by Adedji, Kouessi Norbert, Filipin, Alan, Rihane, Salah Eddine +1
#11B39 #11D61 #11J86 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2210.09699

Abstract

Let b be a positive integer such that 2 ≤ b ≤ 10. In this study, we find all Pell or Pell-Lucas numbers as concatenations of two repdigits in base b. As a corollary, it is show that the largest Pell or Pell-Lucas numbers which can be expressible as a concatenations of two repdigits in base b are P₁₁ = 5741 and Q₅ = 82, respectively.

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