On additive decompositions of the set of primitive roots modulo p

被引：14

作者：

Dartyge, Cecile ^{[1
]}

Sarkoezy, Andras ^{[2
]}

机构：

[1] Univ Nancy 1, Inst Elie Cartan, F-54506 Vandoeuvre Les Nancy, France

[2] Eotvos Lorand Univ, Dept Algebra & Number Theory, H-1117 Budapest, Hungary

来源：

MONATSHEFTE FUR MATHEMATIK | 2013年 / 169卷 / 3-4期

关键词：

Sumset; Additive decomposition; Inverse theorem; Primitive roots;

D O I：

10.1007/s00605-011-0360-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is conjectured that the set of the primitive roots modulo p has no decomposition (modulo p) of the form with , . This conjecture seems to be beyond reach but it is shown that if such a decomposition of exists at all, then , must be around p (1/2), and then this result is applied to show that has no decomposition of the form with , , .C| = 2.

引用

页码：317 / 328

页数：12

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