\(p\)-regularity of the \(p\)-adic valuation of the Fibonacci sequence

by Luis A. Medina and Eric S. Rowland

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 \(m\).

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arXiv Front End

• arXiv