On the Lucas Property of Linear Recurrent Sequences

2016/03/25 by Hao Zhong, Tianxin Cai, Zhong, Hao +1
Mathematics · Physics and Astronomy · #11B39 #11B50 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1603.07863

openalex publication_date 2016/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We say that an arithmetical function S:ℕ→ℤ has Lucas property if for any prime p, S(n)≡ S(n₀)S(n₁)… S(n_r)\pmod p, where n=∑_i=0^rn_ipⁱ, with 0 ≤ n_i ≤ p-1,n,n_i∈ℕ. In this note, we discuss the Lucas property of Fibonacci sequences and Lucas numbers. Meanwhile, we find some other interesting results.

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