On an additive problem of Erdos and Straus, 2

Jean Marc Deshouillers, Gregory A. Freiman

Research output: Contribution to journalArticlepeer-review

Abstract

We denote by sA the set of integers which can be written as a sum of s pairwise distinct elements from A. The set A is called admissible if and only if s ≠ t implies that sA and tA have no element in common. P. Erdos conjectured that an admissible set included in [1, N] has a maximal cardinality when A consists of consecutive integers located at the upper end of the interval [1, N]. The object of this paper is to give a proof of Erdos' conjecture, for sufficiently large N.

Original languageEnglish
Pages (from-to)141-148
Number of pages8
JournalAsterisque
Volume258
StatePublished - 1999

Keywords

  • Admissible sets
  • Arithmetic progressions

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