B2[ g] Sets and a Conjecture of Schinzel and Schmidt

A set of integers A is called a B2[g] set if every integer m has at most g representations of the form m = a + a , with a a and a, a A. We obtain a new lower bound for F(g, n), the largest cardinality of a B2[g] set in {1, . . . , n}. More precisely, we prove that lim infn F (g,n) gn 2 - g where g 0 when g . We show a connection between this problem and another one discussed by Schinzel and Schmidt which can be considered its continuous version.

• Type: Journal
• Year: 2008
• Where: CPC
• Authors: Javier Cilleruelo, Carlos Vinuesa
• Keywords: CPC 2008, Infn, Integer, Largest Cardinality