标题： 对奇数模数覆盖系统的进一步研究 显示英文标题

标题： A further investigation on covering systems with odd moduli

摘要： Erdős于1950年首次提出了覆盖系统的思想。 自从那时以来，这一领域中的大量工作集中在识别满足其模数特定条件的覆盖系统上。 该领域的一个核心未解问题就是著名的奇数覆盖问题。 在本文中，我们研究了该问题的一个变种，其中允许一个奇数整数在覆盖系统中多次作为模数出现，而所有其他模数都是大于1的不同奇数整数。 显示英文摘要

摘要： Erd\H{o}s 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.