A further investigation on covering systems with odd moduli

Key Points

The main focus addresses a unique aspect of the odd covering problem by allowing repetition of one odd integer in the system.
Identifying specific conditions for moduli remains a central task in developing covering systems with practical applications.
The analysis employs theoretical models to explore the implications of using distinct odd integers beyond 1.
Solving this variant of the problem could offer insights into previously unresolved questions in number theory.

Abstract

Erdős first introduced the idea of covering systems in 1950. Since then, much of the work in this area has concentrated on identifying covering systems that meet specific conditions on their moduli. Among the central open problems in this field is the well-known odd covering problem. In this paper, we investigate a variant of that problem, where one odd integer is permitted to appear multiple times as a modulus in the covering system, while all remaining moduli are distinct odd integers greater than 1.

Read Full Paperexternally

Bookmark

View Full Paper

Cite This Study

Bispels et al. (Wed,) studied this question.

synapsesocial.com/papers/69a75c0fc6e9836116a24737 https://doi.org/https://doi.org/10.1016/j.disc.2026.115013

Bookmark

View Full Paper