A non-analytic proof of the Newman-Znám result for disjoint covering systems (Q1086272)

A disjoint covering system is a partition of the set of all integers into a finite number of residue classes. The authors developed recently an elementary lattice parallelotopes technique which avoids the use of complex numbers in proofs of some results concerning disjoint covering systems. In the paper they use this technique to give the first combinatorial proof of a generalization of the well known result that the largest modulus N of a residue class in a disjoint covering system appears at least p times in the system, where p is the smallest prime divisor of N.