A characterization of covering equivalence

DOI10.4064/AA129-4-8zbMATH Open1141.11008arXivmath/0409521OpenAlexW2116638089MaRDI QIDQ5423573

Zhi-Wei Sun, Hao Pan

Publication date: 23 October 2007

Published in: Acta Arithmetica (Search for Journal in Brave)

Abstract: Let A={a_s(mod n_s)}_{s=1}^k and B={b_t(mod m_t)}_{t=1}^l be two systems of residue classes. If |{1le sle k: x=a_s (mod n_s)}| and |{1le tle l: x=b_t (mod m_t)}| 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.

Full work available at URL: https://arxiv.org/abs/math/0409521

zbMATH Keywords

covering systemsystem of residue classescovering equivalenceGraham-O'Bryant conjecture

Mathematics Subject Classification ID

Other combinatorial number theory (11B75) Congruences; primitive roots; residue systems (11A07) Arithmetic progressions (11B25)

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