The conjecture that an odd covering system exists. This was believed to be true and an example was searched for some time, but recent results strongly indicate that this is not the case.

The conjecture that an odd covering system exists. This was believed to be true by Paul Erdös (see Filaseta, M. and Ford, K. and Konyagin, S., On an irreducibility theorem of A. Schinzel associated with coverings of the integers. Illinois J. Math. (2000)) but recent results (see Hough, Robert D. and Nielsen, Pace P., Covering systems with restricted divisibility. Duke Math. J. (2019)) indicate that this is not the case.

In a similar vein to G. Melfi comment, the conjecture that an odd covering system exists. This was believed to be true and an example was searched for some time, but recent results strongly indicate that this is not the case.

The conjecture that an odd covering system exists. This was believed to be true and an example was searched for some time, but recent results strongly indicate that this is not the case.