Solution of the minimum modulus problem for covering systems

DOI10.4007/annals.2015.181.1.6zbMath1344.11015arXiv1307.0874OpenAlexW2963381034MaRDI QIDQ482915

Bob Hough

Publication date: 6 January 2015

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.0874

zbMATH Keywords

probabilistic methodLovász local lemmacovering system of congruencesdistinct moduliminimum modulus problemodd moduli

Mathematics Subject Classification ID

Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Congruences; primitive roots; residue systems (11A07) Arithmetic progressions (11B25) Combinatorial aspects of packing and covering (05B40)

Related Items (19)

Covering systems with odd moduli ⋮ Two questions concerning covering systems ⋮ Boolean Function Analogs of Covering Systems ⋮ Covering systems with large moduli associated with reducible shifts of integer polynomials ⋮ The structure and number of Erdős covering systems ⋮ On the jth smallest modulus of a covering system with distinct moduli ⋮ Covering intervals with arithmetic progressions ⋮ Counterexamples, covering systems, and zero-one laws for inhomogeneous approximation ⋮ On the nearest irreducible lacunary neighbour to an integer polynomial ⋮ Unnamed Item ⋮ Erdős covering systems ⋮ On integers which are the sum of a power of 2 and a polynomial value ⋮ Unnamed Item ⋮ The Erdős-Selfridge problem with square-free moduli ⋮ Covering systems with restricted divisibility ⋮ Unnamed Item ⋮ COMPLEXITY OF SHORT GENERATING FUNCTIONS ⋮ Covering subsets of the integers by congruences ⋮ On the Erdős covering problem: the density of the uncovered set

Uses Software

• PARI/GP

Cites Work

• Some unsolved problems
• A covering system whose smallest modulus is 40
• A covering system with least modulus 25
• Sieving by large integers and covering systems of congruences
• Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x)
• New bounds for $\psi (x)$
• Covering the Set of Integers by Congruence Classes of Distinct Moduli
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