2025/12/03 by Zhongyan Shen, Ross, Tyler, Tianxin Cai +2
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2512.03468
In this paper, we extend the p-adic valuations originally obtained by Carmichael for the sequences obtained by applying Möbius inversion to Lucas sequences to p-adic congruences, from which we immediately derive corresponding congruences for Lucas sequences. As a corollary, we also establish some constraints on the entry point behavior of primes in Lucas sequences, on the basis of which we conjecture the presence of a strong Chebyshev-like bias in real regular Lucas sequences.