• Positive Integer Solutions of the Diophantine Equation $x^2 - L_n xy + (-1)^n y^2 = \pm 5^r$

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/124/03/0301-0313

    • Keywords

       

      Fibonacci numbers; Lucas numbers; diophantine equations

    • Abstract

       

      In this paper, we consider the equation $x^2-L_n xy+(-1)^n y^2=\pm 5^r$ and determine the values of 𝑛 for which the equation has positive integer solutions 𝑥 and 𝑦. Moreover, we give all positive integer solutions of the equation $x^2-L_n xy+(-1)^n y^2=\pm 5^r$ when the equation has positive integer solutions.

    • Author Affiliations

       

      Refik Keskin1 Zafer Şiar2

      1. Sakarya University, Merkezi, 54180 Sakarya, Turkey
      2. Bingöl University, Rektörlüğü, 12000 Bingöl, Turkey
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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