Some results on additive number theory
Some results on additive number theory
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DOI：
10.1090/s0002-9939-1954-0064798-9
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发表时间：
1954-06
期刊：
影响因子：
--
通讯作者：
P. Erdos
中科院分区：
文献类型：
--
作者：
P. Erdos
设0 <a 1 <a2<…是任意整数的无穷序列。用N（ai， N）表示ai的个数。我推测每个序列ai都对应一个序列b；密度0 (i)e。，使得lim n (1/n) n (b;, n)=0)，使得每一个足够大的整数形式为a i +b；洛伦兹2在最近的一篇论文中证明了这个猜想；事实上，他证明了存在一个序列b1，它的必要性质对每一个n都满足
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