关于有限循环群的基的可能阶
On the possible orders of a basis for a finite cyclic group
摘要：
本文证明了Dukes和Herke关于循环群Z_n的基的可能阶的一个猜想，即：对于每个k个\in N，存在一个常数c_k > 0，使得对于所有n个\in N，如果A \subseteq Z_n是阶大于n/k的基，则对于某个整数l \in [1，k]，A的阶在n/l的c_k之内.证明利用了加性数论中关于和集增长的各种结果。
英文摘要：
We prove a conjecture of Dukes and Herke concerning the possible orders of a basis for the cyclic group Z_n, namely : For each k \in N there exists a constant c_k > 0 such that, for all n \in N, if A \subseteq Z_n is a basis of order greater than n/k, then the order of A is within c_k of n/l for some integer l \in [1,k]. The proof makes use of various results in additive number theory concerning the growth of sumsets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
