A characterization of covering equivalence
Abstract
Let A=as(mod ns)s=1k and B=bt(mod mt)t=1l be two systems of residue classes. If |1 s k: x=as (mod ns)| and |1 t l: x=bt (mod mt)| are equal for all integers x, then A and B are said to be covering equivalent. In this paper we characterize the covering equivalence in a simple and new way. Using the characterization we partially confirm a conjecture of R. L. Graham and K. O'Bryant.
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