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First of all i asked for mod primes which is known of chinese remainder theorem that for every finite system is not covering system. I asked for infinite systems.Is there any result that says under what circumstances?
sorry i havent noticed that.Do you know any other general classes because i am interested on that too. Moreover is there any proof with elementary methods that there is at least one prime of the form ak+m (a,m)=1?(for some general classes etc.)