On additive decompositions of the set of primitive roots modulo p

Cécile Dartyge, András Sárközy

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

It is conjectured that the set G of the primitive roots modulo p has no decomposition (modulo p) of the form G = A + B with {pipe}A{pipe} ≥ 2, {pipe}B{pipe} ≥ 2. This conjecture seems to be beyond reach but it is shown that if such a decomposition of G exists at all, then {pipe}A{pipe}, {pipe}B{pipe} must be around p1/2, and then this result is applied to show that G = A + B + C with {pipe}A{pipe} ≥ 2, {pipe}B{pipe} ≥ 2, {pipe}C{pipe} ≥ 2.

Original languageEnglish
Pages (from-to)317-328
Number of pages12
JournalMonatshefte fur Mathematik
Volume169
Issue number3-4
DOIs
Publication statusPublished - Jan 1 2013

Keywords

  • Additive decomposition
  • Inverse theorem
  • Primitive roots
  • Sumset

ASJC Scopus subject areas

  • Mathematics(all)

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