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

A set of integers is called a B2[g] set if every integer m has at most g representations of the form m = a + a2, with a ≤ a2 and a, a2 ∈ . 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 infn→∞ where eg ’ 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.