WHAT WE, BELGIAN’S, CONSIDER TO BE MARKETING

As we are foreign students who will be graduating this June in the field of Business management (Marketing) we wanted to share our knowledge and vision with our fellow Romanian students therefore did we write the following article. We consider marketing to be a universal common language and we strongly hope that our view on this matter will enlighten your entrepreneurial spirit.marketing, marketing mix, product life cycle, swot analysis

A top hat for Moser's four mathemagical rabbits

If the equation 1^k+2^k+...+(m-2)^k+(m-1)^k=m^k has an integer solution with k>1, then m>10^{10^6}. Leo Moser showed this in 1953 by remarkably elementary methods. His proof rests on four identities he derives separately. It is shown here that Moser's result can be derived from a von Staudt-Clausen type theorem (an easy proof of which is also presented here). In this approach the four identities can be derived uniformly. The mathematical arguments used in the proofs were already available during the lifetime of Lagrange (1736-1813).Comment: 7 pages. Meanwhile MacMillan and Sondow showed that Lagrange (1736-1813). can be replaced by Pascal (1623-1662

Integers without large prime factors: from Ramanujan to de Bruijn

A small survey of work done on estimating the number of integers without large prime factors up to around 1950 is provided. Around 1950 N.G. de Bruijn published results that dramatically advanced the subject and started a new era in this topic.Comment: 12 pages, 1 Figur

Nicolaas Govert de Bruijn, the enchanter of friable integers

N.G. de Bruijn carried out fundamental work on integers having only small prime factors and the Dickman-de Bruijn function that arises on computing the density of those integers. In this he used his earlier work on linear functionals and differential-difference equations. We review the relevant work and also some later improvements by others.Comment: 34 pages, 1 Figur

Counting carefree couples

A pair of natural numbers (a,b) such that a is both squarefree and coprime to b is called a carefree couple. A result conjectured by Manfred Schroeder (in his book `Number theory in science and communication') on carefree couples and a variant of it are established using standard arguments from elementary analytic number theory. Also a related conjecture of Schroeder on triples of integers that are pairwise coprime is proved.Comment: Updated version of 2005 update of 2000 version. Improved and expanded presentation. In estimate (2) now only a weaker error term than before is obtaine