A density Chinese Remainder Theorem

2013/02/05 by Jason Gibson, Gibson, Jason
Mathematics · #11B75 (Primary) #11J71 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B75 #msc:11J71

paper · pdf · doi:10.48550/arxiv.1302.0917

9 pages

arxiv created 2013/02/05 · arxiv updated 2013/02/06

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.

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