Erdős-Heilbronn conjecture

Let Ap be a set of residues modulo p, and let h be a positive integer, then

hA={a1+a2++aha1,a2,,ah are distinct elements of A}

has cardinality at least min(p,hk-h2+1). This was conjectured by Erdős and Heilbronn in 1964[1]. The first proof was given by Dias da Silva and Hamidoune in 1994.


  • 1 Paul Erdős and Hans Heilbronn. On the addition of residue classesMathworldPlanetmath modp. Acta Arith., 9:149–159, 1964. 0156.04801.
  • 2 Melvyn B. Nathanson. Additive Number Theory: Inverse Problems and Geometry of Sumsets, volume 165 of GTM. Springer, 1996. 0859.11003.
Title Erdős-Heilbronn conjecture
Canonical name ErdHosHeilbronnConjecture
Date of creation 2013-03-22 13:38:15
Last modified on 2013-03-22 13:38:15
Owner bbukh (348)
Last modified by bbukh (348)
Numerical id 10
Author bbukh (348)
Entry type Theorem
Classification msc 11B75
Related topic CauchyDavenportTheorem