$p$-regularity of the $p$-adic valuation of the Fibonacci sequence

Luis A. Medina; Eric Rowland

$p$-regularity of the $p$-adic valuation of the Fibonacci sequence

Number Theory 2015-10-15 v4

Authors: Luis A. Medina , Eric Rowland

Abstract

We show that the $p$ -adic valuation of the sequence of Fibonacci numbers is a $p$ -regular sequence for every prime $p$ . For $p \neq 2, 5$ , we determine that the rank of this sequence is $\alpha(p) + 1$ , where $\alpha(m)$ is the restricted period length of the Fibonacci sequence modulo $m$ .

Keywords

fibonacci sequence p-adic valuation p-regular sequence restricted period length prime numbers

Cite

@article{arxiv.0910.2907,
  title  = {$p$-regularity of the $p$-adic valuation of the Fibonacci sequence},
  author = {Luis A. Medina and Eric Rowland},
  journal= {arXiv preprint arXiv:0910.2907},
  year   = {2015}
}

Comments

7 pages; publication version

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