Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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A COMPLETE FORMULA FOR THE ORDER OF APPEARANCE OF THE POWERS OF LUCAS NUMBERS

  • Received : 2015.09.06
  • Published : 2016.07.31
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Abstract

Let $F_n$ and $L_n$ be the nth Fibonacci number and Lucas number, respectively. The order of appearance of m in the Fibonacci sequence, denoted by z(m), is the smallest positive integer k such that m divides $F_k$. Marques obtained the formula of $z(L^k_n)$ in some cases. In this article, we obtain the formula of $z(L^k_n)$ for all $n,k{\geq}1$.

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References

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Cited by

  1. The order of appearance of factorials in the Fibonacci sequence and certain Diophantine equations pp.1588-2829, 2018, https://doi.org/10.1007/s10998-018-0268-6