On infinite additive complements

发布时间：2018-04-03 08:55

  本文选题：additive　切入点：complements　出处：《Science China(Mathematics)》2017年10期

【摘要】：Two infinite sequences A and B of non-negative integers are called infinite additive complements if their sum contains all sufficiently large integers. For a sequence T of non-negative integers, let T(x) be the number of terms of T not exceeding x. In 1994, S′ark¨ozy and Szemer′edi confirmed a conjecture of Danzer by proving that, for infinite additive complements A and B, if lim sup A(x)B(x)/x 1, then A(x)B(x)-x → +∞ as x → +∞. In this paper, it is proved that, if A and B are infinite additive complements with lim sup A(x)B(x)/x(4 2～(1/2) + 2)/7 = 1.093 …, then(A(x)B(x)-x)/min{A(x), B(x)} → +∞ as x → +∞.
[Abstract]:Two infinite sequences A and B of non-negative integers are called infinite additive complements if their sum contains all sufficiently large integers.For a sequence T of non-negative integers, let the number of terms of T not exceeding x.Ozy and Szemer'edi confirmed a conjecture of Danzer by proving that, for infinite additive complements A and B, if lim sup A(x)B(x)/x 1, then A(x)B(x)-x 鈭，

本文编号：1704503