Problem Statement
Is there a covering system all of whose moduli are odd?
Categories:
Number Theory Covering Systems
Progress
Key Results
Balister, Bollobás, Morris, Sahasrabudhe, and Tiba: No covering system exists where all moduli are both odd AND squarefree.
Hough and Nielsen: At least one modulus must be divisible by 2 or 3. If an odd system exists, its LCM must be divisible by 9 or 15.
Source: erdosproblems.com/7 | Last verified: January 13, 2026