Главная

Carl Pomerance

  1. On sets of integers which are both sum-free and product-free.

    Пнд, 01/09/2012 - 15:01 — SomNambul
    Authors: Jeffrey C. Lagarias, Par Kurlberg, Carl Pomerance
    Subjects: Number Theory
    Abstract

    We consider sets of positive integers containing no sum of two elements in
    the set and also no product of two elements. We show that the upper density of
    such a set is strictly smaller than 1/2 and that this is best possible.
    Further, we also find the maximal order for the density of such sets that are
    also periodic modulo some positive integer.

  2. Product-free sets with high density.

    Пт, 07/29/2011 - 15:01 — SomNambul
    Authors: Jeffrey C. Lagarias, Par Kurlberg, Carl Pomerance
    Subjects: Number Theory
    Abstract

    We show that there are sets of integers with asymptotic density arbitrarily
    close to 1 in which there is no solution to the equation ab=c, with a,b,c in
    the set. We also consider some natural generalizations, as well as a specific
    numerical example of a product-free set of integers with asymptotic density
    greater than 1/2.

Math-arch

RSS-материал