The existence of odd covering system with distinct moduli is a famous open question proposed by [Erdős and Selfridge][1].

I wonder whether a restricted condition for the problem that odd covering system without modulus 3 is also an open problem. That is to say, whether an incongruent covering system with the minimum modulus greater than 3 and whose moduli are odd exist or not.

Thanks.


p.s. The same question was posted on [MSE][2]. If I get an answer from one site I would delete the other. 


  [1]: https://en.wikipedia.org/wiki/Covering_system#Systems_of_odd_moduli
  [2]: https://math.stackexchange.com/questions/4394827/odd-covering-system-without-modulus-3-pmod3