Abstract
The aim of this text is to calculate the p-adic valuation v p (f n ) where p is a prime number, and (f n ) n≥0 the Fibonacci sequence: f 0 = 0, f 1 = 1, f n+1 = f n + f n−1, n ≥ 1. We obtain this information “in one go” using the p-adic numbers; this enlights the nature of the (well known) result.
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References
J. H. Halton, “On the divisibility properties of Fibonacci numbers,” Fibonacci Q. 4(3), 217–240 (1966).
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Faisant, A. The p-adic golden section. P-Adic Num Ultrametr Anal Appl 6, 284–292 (2014). https://doi.org/10.1134/S2070046614040037
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DOI: https://doi.org/10.1134/S2070046614040037