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

Abstract

We show that the $p$-adic valuation of the sequence of Fibonacci numbers is a $p$-regular sequence for every prime $p$. For $p\ne 2,5$, 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 $m$.

7 pages; publication version

References in corpus (1)

• The p-adic valuations of sequences counting alternating sign matrices

Cited by in corpus (1)

• On the k-regularity of the k-adic valuation of Lucas sequences