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

Medina, Luis; Rowland, Eric

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

Medina, Luis; Rowland, Eric

2015 • In Fibonacci Quarterly, 53 (3), p. 265-271

Peer reviewed

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https://hdl.handle.net/2268/185411

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Keywords :

Fibonacci sequence; valuation; regular sequence

Abstract :

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

Disciplines :

Mathematics

Author, co-author :

Medina, Luis

Rowland, Eric ; Université de Liège > Département de mathématique > Mathématiques discrètes

Language :

English

Title :

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

Publication date :

August 2015

Journal title :

Fibonacci Quarterly

ISSN :

0015-0517

Publisher :

Fibonacci Association, United States - California

Volume :

Issue :

Pages :

265-271

Peer reviewed :

Peer reviewed

Available on ORBi :

since 01 September 2015

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Bibliography

J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical Computer Science, 98 (1992), 163-197.
T. Amdeberhan, D. Manna, and V. Moll, The 2-adic valuation of Stirling numbers, Experimental Mathematics, 17 (2008), 69-82.
T. Amdeberhan, L. A. Medina, and V. Moll, Asymptotic valuations of sequences satisfying first order recurrences, Proceedings of the American Mathematical Society, 137 (2009), 885-890.
J. P. Bell, p-adic valuations and k-regular sequences, Discrete Mathematics, 307 (2007), 3070-3075.
H. Cohn, 2-adic behavior of numbers of domino tilings, The Electronic Journal of Combinatorics, 6 (1999), #R14.
F. G. Dorais and D. Klyve, A Wiefreich prime search up to 6.7 × 1015, Journal of Integer Sequences, 14 (2011), 11.9.2.
J. D. Fulton and W. L. Morris, On arithmetical functions related to the Fibonacci numbers, Acta Arithmetica, 16 (1969), 105-110.
T. Lengyel, On the divisibility by 2 of the Stirling numbers of the second kind, The Fibonacci Quarterly, 32.3 (1994), 194-201.
T. Lengyel, The order of the Fibonacci and Lucas numbers, The Fibonacci Quarterly, 33.3 (1995), 234-239.
R. J. McIntosh and E. L. Roettger, A search for Fibonacci-Wieferich and Wolstenholme primes, Mathematics of Computation, 76 (2007), 2087-2094.
A. Postnikov and B. E. Sagan, What power of two divides a weighted Catalan number?, Journal of Combinatorial Theory, Series A, 114 (2007), 970-977.
PrimeGrid, http://www.primegrid.com.
M. Renault, The Fibonacci sequence under various moduli, Master's Thesis, Wake Forest University (1996). http://webspace.ship.edu/msrenault/fibonacci/FibThesis.pdf.
D. W. Robinson, The Fibonacci matrix modulo m, The Fibonacci Quarterly, 1.1 (1963), 29-36.
Z. Shu and J.-Y. Yao, Analytic functions over Zp and p-regular sequences, Comptes Rendus Mathematique, 349 (2011), 947-952.
X. Sun and V. Moll, The p-adic valuation of sequences counting alternating sign matrices, Journal of Integer Sequences, 12 (2009), 09.3.8.
X. Sun and V. Moll, A binary tree representation for the 2-adic valuation of a sequence arising from a rational integral, Integers: The Electronic Journal of Combinatorial Number Theory, 10 (2010), 211-222.
D. D. Wall, Fibonacci series modulo m, The American Mathematical Monthly, 67 (1960), 525-532.