Displaying similar documents to “Corrections to 'Asymptotic behaviour of some infinite products involving prime numbers' (Acta Arith. 75 (1996), 339-350)”

Uniqueness of Factoring an Integer and Multiplicative Group Z/pZ*

Hiroyuki Okazaki, Yasunari Shidama (2008)

Formalized Mathematics

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In the [20], it had been proven that the Integers modulo p, in this article we shall refer as Z/pZ, constitutes a field if and only if Z/pZ is a prime. Then the prime modulo Z/pZ is an additive cyclic group and Z/pZ* = Z/pZ{0is a multiplicative cyclic group, too. The former has been proven in the [23]. However, the latter had not been proven yet. In this article, first, we prove a theorem concerning the LCM to prove the existence of primitive elements of Z/pZ*. Moreover we prove the...

A prime factor theorem for a generalized direct product

Wilfried Imrich, Peter F. Stadler (2006)

Discussiones Mathematicae Graph Theory

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We introduce the concept of neighborhood systems as a generalization of directed, reflexive graphs and show that the prime factorization of neighborhood systems with respect to the the direct product is unique under the condition that they satisfy an appropriate notion of thinness.

On the sumset of the primes and a linear recurrence

Christian Ballot, Florian Luca (2013)

Acta Arithmetica

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Romanoff (1934) showed that integers that are the sum of a prime and a power of 2 have positive lower asymptotic density in the positive integers. We adapt his method by showing more generally the existence of a positive lower asymptotic density for integers that are the sum of a prime and a term of a given nonconstant nondegenerate integral linear recurrence with separable characteristic polynomial.