Sieving by large integers and covering systems of congruences

DOI10.1090/S0894-0347-06-00549-2zbMath1210.11020arXivmath/0507374MaRDI QIDQ3420416

Kevin Ford, Michael Filaseta, Gang Yu, Carl B. Pomerance, Sergei V. Konyagin

Publication date: 2 February 2007

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0507374

zbMATH Keywords

sieve methodscovering systems of congruences

Mathematics Subject Classification ID

Applications of sieve methods (11N36) Congruences; primitive roots; residue systems (11A07) Density, gaps, topology (11B05) Arithmetic progressions (11B25)

Related Items (21)

Zero-sum problems for abelian \(p\)-groups and covers of the integers by residue classes ⋮ Covering systems in number fields ⋮ Covering systems with odd moduli ⋮ Covering modules by proper submodules ⋮ Essential positive covers of the cube ⋮ Covering systems with large moduli associated with reducible shifts of integer polynomials ⋮ The structure and number of Erdős covering systems ⋮ Composite values of shifted exponentials ⋮ Covering intervals with arithmetic progressions ⋮ Counterexamples, covering systems, and zero-one laws for inhomogeneous approximation ⋮ Erdős covering systems ⋮ Solution of the minimum modulus problem for covering systems ⋮ An estimate for the probability of dependent events ⋮ Unnamed Item ⋮ A covering system with least modulus 25 ⋮ Covers of the integers with odd moduli and their applications to the forms $x^{m}-2^{n}$ and $x^{2}-F_{3n}/2$ ⋮ The Erdős-Selfridge problem with square-free moduli ⋮ Covering systems with restricted divisibility ⋮ A covering system whose smallest modulus is 40 ⋮ Covering subsets of the integers by congruences ⋮ On the Erdős covering problem: the density of the uncovered set

Cites Work

• Integers without large prime factors
• The distribution of integers with a divisor in a given interval
• Approximate formulas for some functions of prime numbers
• Covering systems of congruences, a negative result
• FINITE COVERS OF GROUPS BY COSETS OR SUBGROUPS
• On Weird and Pseudoperfect Numbers
• Unsolved problems in number theory
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