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

2026/07/21 by Tyler Ross, Zhongyan Shen, Tianxin Cai
Physics and Astronomy · Mathematics · #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #Advanced Mathematical Identities

paper · doi:10.1080/00150517.2026.2656703

Abstract

In this paper, we extend the p-adic valuations of the Möbius duals of Lucas sequences, originally obtained by Carmichael for regular Lucas sequences, to irregular Lucas sequences. We conclude with a brief observation about the relationship of these valuations to the existence of Wall-Sun-Sun primes.

Citations

• Theorie des Fonctions Numeriques Simplement Periodiques
• The <i>p</i> -adic Valuation of Lucas Sequences When <i>p</i> Is a Special Prime
• The <i>p</i> -Adic Valuation of Lucas Sequences
• The Order of the Fibonacci and Lucas Numbers

Related

• The p-adic Valuations of Möbius Duals of Lucas Sequences
• The <i>p</i> -adic Valuation of Lucas Sequences When <i>p</i> Is a Special Prime
• Cyclotomic Congruences and Lucas Sequences
• The <i>p</i> -Adic Valuation of Lucas Sequences
• On k-regularity of sequences of valuations and last nonzero digits