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Displaying similar documents to “Prime numbers with a fixed number of one bits or zero bits in their binary representation.”

Pocklington's Theorem and Bertrand's Postulate

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.

Prime mappings, number of factors and binary operations

Eric K. van Douwen

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CONTENTS1. Interesting mappings on finite powers..................................................... 52. Results.................................................................................................................... 63. Conventions and notation.................................................................................... 84. βω-spaces.............................................................................................................. 85. Canonical partition...

On the Properties of the Möbius Function

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...