Displaying similar documents to “Primes in arithmetic progressions to spaced moduli”

On non-intersecting arithmetic progressions

Régis de la Bretèche, Kevin Ford, Joseph Vandehey (2013)

Acta Arithmetica

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We improve known bounds for the maximum number of pairwise disjoint arithmetic progressions using distinct moduli less than x. We close the gap between upper and lower bounds even further under the assumption of a conjecture from combinatorics about Δ-systems (also known as sunflowers).

Topological aspects of infinitude of primes in arithmetic progressions

František Marko, Štefan Porubský (2015)

Colloquium Mathematicae

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We investigate properties of coset topologies on commutative domains with an identity, in particular, the 𝓢-coprime topologies defined by Marko and Porubský (2012) and akin to the topology defined by Furstenberg (1955) in his proof of the infinitude of rational primes. We extend results about the infinitude of prime or maximal ideals related to the Dirichlet theorem on the infinitude of primes from Knopfmacher and Porubský (1997), and correct some results from that paper. Then we determine...