The <i>p</i> -Adic Valuation of Lucas Sequences

2016/05/01 by Carlo Sanna · 2 citations
Mathematics · Physics and Astronomy · #advanced mathematical theories #Advanced Mathematical Theories and Applications #Mathematical Dynamics and Fractals

paper · doi:10.1080/00150517.2016.12427821

Abstract

Let (un)n≥0 be a nondegenerate Lucas sequence with characteristic polynomial X2- aX - b, for some relatively prime integers a and b. For each prime number p and each positive integer n, we give simple formulas for the p-adic valuation νp(un), in terms of νp(n) and the rank of apparition of p in (un)n≥0. This generalizes a previous result of Lengyel on the p-adic valuation of Fibonacci numbers, and also the folkloristic “lifting-the-exponent lemma”.

Citations

• Theorie des Fonctions Numeriques Simplement Periodiques
• The Order of the Fibonacci and Lucas Numbers

Cited by

• The <i>p</i> -adic Valuations of Möbius Duals of Lucas Sequences
• The p-adic Valuations of Möbius Duals of Lucas Sequences

Related

• The <i>p</i> -adic Valuation of Lucas Sequences When <i>p</i> Is a Special Prime
• On alternative definition of Lucas atoms and their p-adic valuations
• Cyclotomic Congruences and Lucas Sequences
• The <i>p</i> -adic Valuations of Möbius Duals of Lucas Sequences
• The p-adic Valuations of Möbius Duals of Lucas Sequences