On the structure of sets with many k-term arithmetic progressions
(2009)
Acta Arithmetica
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Displaying similar documents to “Solving a ± b = 2c in elements of finite sets”
On the structure of sets with many k-term arithmetic progressions
A generalization of Freiman's 3k-3 Theorem
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Some results on Oppenheim's "Factorisatio Numerorum" function
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We investigate the reverse mathematical strength of Turing determinacy up to Σ₅⁰, which is itself not provable in second order arithmetic.
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).
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M. Artigue, E. Isambert, M. Perrin, A. Zalc (1978)
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Textes & documents - A new source for medieval mathematics in the iberian peninsula: the commercial arithmetic in Ms 10106 (Biblioteca Nacional, Madrid)
Javier Docampo Rey (2009)
Revue d'histoire des mathématiques
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This paper contains a critical edition of a short commercial arithmetic written in Castilian (ca. 1400). The manuscript has certain characteristic features, like the presence of composite fractions, that distinguishes it from other known treatises of the Iberian peninsula. The document appears to improve considerably our knowledge of the origins and the transmission of vernacular commercial arithmetic in Europe.
Sums of multiplicative function in special arithmetic progressions
Bin Feng (2019)
Czechoslovak Mathematical Journal
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We find, via the Selberg-Delange method, an asymptotic formula for the mean of arithmetic functions on certain APs. It generalizes a result due to Cui and Wu (2014).
Arithmetic progressions in sums of subsets of sparse sets
Tomasz Schoen (2011)
Acta Arithmetica
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Arithmetic functions on Beatty sequences
Abercrombie Alex G., Banks William D., Shparlinski Igor E. (2009)
Acta Arithmetica
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On non-intersecting arithmetic progressions
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Acta Arithmetica
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