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arXiv · 2512.03481

The $p$-adic Valuations of M\"obius Duals of Lucas Sequences

Tyler Ross·Zhongyan Shen·Tianxin Cai
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Abstract

In this paper, we extend the $p$-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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Tyler Ross, Zhongyan Shen, Tianxin Cai. 2025-12-03. The $p$-adic Valuations of M\"obius Duals of Lucas Sequences. https://arxiv.org/abs/2512.03481

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