# Covering systems with restricted divisibility

## TL;DR

This paper proves that any covering system with distinct moduli must include a modulus divisible by 2 or 3, revealing a fundamental restriction on the structure of such systems.

## Contribution

It establishes a new necessary condition for the existence of distinct covering systems, showing they must involve moduli divisible by 2 or 3.

## Key findings

- Every distinct covering system has a modulus divisible by 2 or 3.
- Provides a fundamental restriction on the structure of covering systems.
- Advances understanding of divisibility constraints in covering systems.

## Abstract

We prove that every distinct covering system has a modulus divisible by either 2 or 3.