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OPEN
For which $n$ is there a covering system $\{ a_d\pmod{d} : d\mid n\}$ such that if $x\equiv a_{d_1}\pmod{d_1}$ and $x\equiv a_{d_2}\pmod{d_2}$ then $(d_1,d_2)=1$?
The density of such $n$ is zero.