Some results on additive number theory

Abstract

Let 0 <a 1 <a2< . . . be any infinite sequence of integers . Denote by N(ai , n) the number of ai S n . I conjectured that to every sequence ai there corresponds a sequence b ; of density 0 (i .e ., such that lim n (1/n)N(b;, n)=0) so that every sufficiently large integer is of the form a i +b;. Lorentz 2 in a recent paper proved this conjecture ; in fact, he showed that there exists a sequence b1 with the required property satisfying for every n

Locations

• Proceedings of the American Mathematical Society - View - PDF