All Random Solved Random Open
Do there exist $n$ with an associated covering system $a_d\pmod{d}$ on the divisors of $n$ (so that $d\mid n$ for all $d$ in the system), such that if \[x\equiv a_d\pmod{d}\textrm{ and }x\equiv a_{d'}\pmod{d'}\] then $(d,d')=1$? For a given $n$ what is the density of the integers which do not satisfy any of the congruences?
The density of such $n$ is zero. Erdős and Graham believed that no such $n$ exist.