On a problem of sidon in additive number theory, and on some related problems
On a problem of sidon in additive number theory, and on some related problems
复制标题
DOI：
10.1112/jlms/s1-16.4.212
复制
发表时间：
1941-10
影响因子：
1.2
通讯作者：
P. Erdös;P. Turán
中科院分区：
文献类型：
--
作者：
P. Erdös;P. Turán
纪念S.Sidon。设0是所有n>；1的0，线性f(N)‘ne=0是所有t>；0。在本说明中，我将构建这样一个序列。事实上，我的序列将满足(1)0 L。(c将表示适当的正绝对常数。)(1)似乎不可能得到很大的加强。Turan和我猜想2)如果f(N)>；0对所有n>；N0成立，则Lim sup f(N)=-；这个猜想似乎很难证明。一个更有力的猜想如下：设a，2k。在这种情况下，b(K)仅仅是区间(2k，2k}1)的所有整数。而且，这也足以证明f(N)>；0适用于所有的口头交流。
To the memory of S. Sidon. Let 0 0 for all n > 1 and lim f(n)'nE = 0 for all t > 0. In the present note, I will construct such a sequence. In fact, my sequence will satisfy (1) 0 l. (The c's will denote suitable positive absolute constants .) It seems probable that (1) can not be strengthened very much. TURAN and I conjectured 2) that if f(n) > 0 for all n > n0 then lim sup f(n)=-; this conjecture seems very hard to prove. A still stronger conjecture would be the following : Let a, 2k. In this case the b(k) are simply all the integers of the interval (2 k, 2k} 1). Also, it is clearly enough to show that f(n) > 0 for all 1) Oral communication .