A density Chinese Remainder Theorem
Number Theory
2013-02-06 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1302.0917,
title = {A density Chinese Remainder Theorem},
author = {Jason Gibson},
journal= {arXiv preprint arXiv:1302.0917},
year = {2013}
}
Comments
9 pages