Restricted sums in a field
Restricted sums in a field
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DOI：
10.4064/aa102-3-3
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发表时间：
2002
期刊：
影响因子：
0.7
通讯作者：
Q. Hou;Zhi-Wei Sun
中科院分区：
文献类型：
--
作者：
Q. Hou;Zhi-Wei Sun
设Zp=Z/Pz表示模素数p的所有剩余类的域。[Eh]和[Gu])猜想，对于ZP的每个非空子集A，至少有Min{p，2|A|−3}个模为p的剩余类可以表示为A的两个不同元素的和。这一猜想已经持续了30年，直到J.A.Dias da Silva和Y.O.Hamidoune([DH])借助对称群的表示理论证明了以下结果。
Let Zp = Z/pZ stand for the field of all residue classes modulo prime p. In 1964 P. Erdös and H. Heilbronn (cf. [EH] and [Gu]) conjectured that for each nonempty subset A of Zp there are at least min{p, 2|A| − 3} residue classes modulo p that can be written as the sum of two distinct elements of A. This had been open for thirty years until J. A. Dias da Silva and Y. O. Hamidoune ([DH]) proved the following result with the help of the representation theory of symmetric groups.