Lucas numbers of the form (2t/k)

  • Nurettin Irmak Niğde Ömer Halisdemir University, Art and Science Faculty, Mathematics Department, Niğde, Turkey
  • László Szalay J. Selye University, Department of Mathematics and Informatics, Komarno
Keywords: Lucas number, binomial coefficient, diophantine equation

Abstract

Let Lm denote the mth Lucas number. We show that the solutions to the diophantine equation (2t/k) = Lm, in non-negative integers t, k ≤ 2t−1, and m, are (t, k, m) = (1, 1, 0), (2, 1, 3), and (a, 0, 1) with non-negative integers a.

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Published
2019-08-09
Section
Articles