Combinatorial designs have been used to construct digital fingerprint codes. Here, a new constructive algorithm for an anticollusion fingerprint code based on group-divisible designs is presented. These codes are easy to construct and available for a large number of individuals, which is important from a business point of view. Group-divisible designs have not been used previously as a tool for...

We study the possible cardinalities of the divisible part of G/K when the cardinality of K is known and when, for all countable subgroups C of G, the divisible part of G/C is countable.

cet article est consacréà l’étude du dialogue dans enfance, récit autobiographique de nathalie sarraute qui contient des souvenirs de ses onze premières années. l’une des originalités de ce récit, se base sur la présence de deux voix narratives qui dialoguent tout au long du récit. l’une de ces dernières, joue le rôle d’une narratrice et l’autre représente le côté conscient de l’auteur qui suiv...

Jenkins in 2003 showed that every odd perfect number is divisible by a prime exceeding 107. Using the properties of cyclotomic polynomials, we improve this result to show that every perfect number is divisible by a prime exceeding 108.

SHORTLY BEFORE THE INDUSTRIAL REVOLUTION the English philosopher John Locke put forward a theory of property that reflected the emerging capitalist system. This theory has often been interpreted as supposing that we, the human race, live on a frontier with the natural world, looking across to plentiful resources in an as yet un-tamed and un-owned wilderness. In the 1960s Kenneth Boulding, an ec...

In this article, we formalize the definition of divisible Z-module and its properties in the Mizar system [3]. We formally prove that any non-trivial divisible Z-modules are not finitely-generated. We introduce a divisible Z-module, equivalent to a vector space of a torsion-free Z-module with a coefficient ring Q. Z-modules are important for lattice problems, LLL (Lenstra, Lenstra and Lovász) b...

Let M be an o–minimal expansion of a real closed field. It is known that a definably connected abelian group is divisible. In this note, we show that a definably compact definably connected group is divisible.