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
收藏
页码：317 / 328
页数：12
相关论文
共 50 条
  • [21] On additive decompositions of the set of primes
    J.-C. Puchta
    Archiv der Mathematik, 2002, 78 : 24 - 25
  • [22] DECOMPOSITIONS OF ADDITIVE SET FUNCTIONS
    BELL, WC
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 23 (06): : A585 - A585
  • [23] On additive decompositions of primitive elements in finite fields
    She, Yue-Feng
    Wu, Hai-Liang
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2024, 20 (02) : 603 - 613
  • [24] On consecutive primitive nth roots of unity modulo q
    Brazelton, Thomas
    Harrington, Joshua
    Kannan, Siddarth
    Litman, Matthew
    JOURNAL OF NUMBER THEORY, 2017, 174 : 494 - 504
  • [25] LEAST PRIMITIVE ROOTS MODULO THE SQUARE OF A PRIME IDEAL
    HINZ, JG
    MATHEMATIKA, 1986, 33 (66) : 244 - 252
  • [26] On the number of semi-primitive roots modulo n
    Goswami, Pinkimani
    Singh, Madan Mohan
    NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2015, 21 (04) : 48 - 55
  • [27] Square roots modulo p
    Tornaría, G
    LATIN 2002: THEORETICAL INFORMATICS, 2002, 2286 : 430 - 434
  • [28] PRIMITIVE ROOTS MODULO A PRIME AS CONSECUTIVE TERMS OF AN ARITHMETIC PROGRESSION
    VEGH, E
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1969, 235 : 185 - &
  • [29] On the computation of cube roots modulo p
    Müller, S
    HIGH PRIMES AND MISDEMEANOURS: LECTURES IN HONOUR OF THE 60TH BIRTHDAY OF HUGH COWIE WILLIAMS, 2004, 41 : 293 - 304
  • [30] On the average of the least primitive root modulo p
    Elliott, PDTA
    Murata, L
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1997, 56 : 435 - 454
12345