Finite set of congruences

Finite set of congruences

Is it true that for every $c$ there is a finite set of congruences
$a_i(mod\,\,n_i) , c = n_1<n_2<n_3<...........<n_k \,\,\, (1)\\ $
So that every integer satisfies at least one of the congruence (1)