Are there $n$ such that there is a covering system with moduli the divisors of $n$ which is 'as
disjoint as possible'?
That is, for all $d\mid n$ with $d>1$ there is an associated $a_d$ such that every integer is
congruent to some $a_d\pmod{d}$, and if there is some integer $x$ with
\[x\equiv a_d\pmod{d}\textrm{ and }x\equiv a_{d'}\pmod{d'}\]then $(d,d')=1$.
The density of such $n$ is zero. Erdős and Graham believed that no such $n$ exist.
Adenwalla [Ad25] has proved there are no such $n$.
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