[REOPENED]
I'd like to suggest reopening Covering systems. As I wrote in a comment,
Why is this closed? Covering systems are a recognized area of research in Number Theory. It's known that in an irredundant cover with a modulus divisible by a prime $p$ there are at least $p$ moduli divisible by $p$. This asks whether, if there is a modulus divisible by a power of a prime $p$, there are at least $p$ moduli divisible by that power of $p$. Seems like a reasonable research question to me.
[Also, I think I can answer it.]
