Sieving by prime powers
P. Gallagher (1974)
Acta Arithmetica
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P. Gallagher (1974)
Acta Arithmetica
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K. Ramachandra (1971)
Acta Arithmetica
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K. Szymiczek (1964)
Colloquium Mathematicae
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Marco Riccardi (2006)
Formalized Mathematics
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The first four sections of this article include some auxiliary theorems related to number and finite sequence of numbers, in particular a primality test, the Pocklington's theorem (see [19]). The last section presents the formalization of Bertrand's postulate closely following the book [1], pp. 7-9.
Magdalena Jastrzebska, Adam Grabowski (2006)
Formalized Mathematics
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We formalized some basic properties of the Möbius function which is defined classically as [...] as e.g., its multiplicativity. To enable smooth reasoning about the sum of this number-theoretic function, we introduced an underlying many-sorted set indexed by the set of natural numbers. Its elements are just values of the Möbius function.The second part of the paper is devoted to the notion of the radical of number, i.e. the product of its all prime factors.The formalization (which is...
Jiahai Kan (2004)
Acta Arithmetica
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Artūras Dubickas, Andrius Stankevičius (2007)
Acta Arithmetica
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Vera M. Jesus, Paulo Canas Rodrigues, João Tiago Mexia (2007)
Discussiones Mathematicae Probability and Statistics
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Commutative Jordan algebras are used to drive an highly tractable framework for balanced factorial designs with a prime number p of levels for their factors. Both fixed effects and random effects models are treated. Sufficient complete statistics are obtained and used to derive UMVUE for the relevant parameters. Confidence regions are obtained and it is shown how to use duality for hypothesis testing.
Florian Luca, Francesco Pappalardi (2007)
Acta Arithmetica
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Paul Erdös, Aleksandar Ivić (1982)
Publications de l'Institut Mathématique
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Richard Hudson (1973)
Acta Arithmetica
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Nyman, Bertil, Nicely, Thomas R. (2003)
Journal of Integer Sequences [electronic only]
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Jianya Liu, Kai-Man Tsang (2005)
Acta Arithmetica
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Xuan Tizuo (1988)
Publications de l'Institut Mathématique
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Müller, Tom (2005)
Journal of Integer Sequences [electronic only]
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