Work

The local Dold congruence for Fibonacci and Lucas sequences

Year: 2026

Type: preprint

Abstract: We discuss local properties of the classical Fibonacci and Lucas sequences, characterising in both cases those primes~$p$ for which the~$p$-part satisfies the Dold congruences or is realizable. We calculate an exact `repair' multiplier in each case and determine the relative prime densities of the Dold, realizable, almost Dold, and almost realizable prime sets. In that order, the four densities are~$(\frac34,\frac13,1,\frac13)$ for the Lucas sequence and~$(\frac12,\frac12,1,1)$ for the Fibonacci sequence.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.24544

Authors: Chuysurichay, Sompong, Jaidee, Sawian, Panraksa, Chatchawan, Ward, Thomas

Institutions: Prince of Songkla University, Khon Kaen University, Mahidol University, Durham University

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Khon Kaen University

OpenAlex ID: W7214040976

Cites:

Cited by:

Related to: 10