The $p$-adic Valuations of M\"obius Duals of Lucas Sequences
Tyler Ross, Zhongyan Shen, Tianxin Cai
TL;DR
This paper extends the understanding of $p$-adic valuations of M"obius duals from regular to irregular Lucas sequences and explores their connection to Wall-Sun-Sun primes.
Contribution
It generalizes previous results on $p$-adic valuations to irregular Lucas sequences and discusses their relation to special primes.
Findings
Extended $p$-adic valuation formulas to irregular Lucas sequences
Identified potential links to Wall-Sun-Sun primes
Provided new insights into Lucas sequence properties
Abstract
In this paper, we extend the -adic valuations of the M\"obius 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.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Analytic Number Theory Research · Advanced Mathematical Identities