  Given collections A and B of residue classes modulo m and n, respectively, we
investigate conditions on A and B that ensure that, for at least some a in A
and b in B, the linear system x = a mod m, x = b mod n has an integer solution,
and we quantify the number of such admissible pairs (a,b). The special case
where A and B consist of intervals of residue classes has application to the
Lonely Runner Conjecture.
