2019/08/01 by Christian Ballot · 5 citations
Mathematics · #Combinatorics #Economics #Finance #Lucas sequence #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #Mathematics #Prime (order theory) #Prime number #Valuation (finance) #advanced mathematical theories
paper · doi:10.1080/00150517.2019.12427650
published in The Fibonacci Quarterly 57(3), 265-275 (The Fibonacci Association)
openalex publication_date 2019/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
The behavior of the p-adic valuation of the terms of Lucas sequences has basically been known since the seminal work of Lucas in 1878, although it has been revisited many times with partial or complete results. However, the assumption always seems to be that the parameters P and Q of the recursion are coprime, i.e., that the sequence is regular. We complete the picture by evaluating the valuation of Lucas sequences with respect to a special prime, i.e., one dividing P and Q.