A density Chinese Remainder Theorem [article]

Jason Gibson
2013 arXiv   pre-print
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.
arXiv:1302.0917v1 fatcat:v5pfz43govdqjgspziegmqrtee