Product-free sets with high density
  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. 
Par Kurlberg, Jeffrey C. Lagarias, Carl Pomerance
math.NT