Some results on Oppenheim's "Factorisatio Numerorum" function
Florian Luca, Anirban Mukhopadhyay, Kotyada Srinivas (2010)
Acta Arithmetica
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Florian Luca, Anirban Mukhopadhyay, Kotyada Srinivas (2010)
Acta Arithmetica
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Brahmagupta
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Augustus DeMorgan
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Andrzej Grzegorczyk (1956)
Fundamenta Mathematicae
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(2009)
Acta Arithmetica
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John Leslie
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M. Artigue, E. Isambert, M. Perrin, A. Zalc (1978)
Fundamenta Mathematicae
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Yahya Ould Hamidoune, Alain Plagne (2002)
Acta Arithmetica
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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).
Antonio Montalbán, Richard A. Shore (2016)
Fundamenta Mathematicae
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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.
Yong-Gao Chen (2005)
Acta Arithmetica
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Abercrombie Alex G., Banks William D., Shparlinski Igor E. (2009)
Acta Arithmetica
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Hédi Daboussi, András Sárközy (2003)
Acta Arithmetica
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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.
Slavyana Geninska (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
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This is a small survey paper about connections between the arithmetic and geometric properties in the case of arithmetic Fuchsian groups.