---
tag: FJQ34W02Q9
kind: statement
role: proposition
name: Behrend's theorem
sources:
  - wikipedia: en:59852572@r1329702874
    locator: Behrend's theorem
    note: adopted
    mention: wikipedia://en/59852572
    sections: [Statement]
same_as:
  wikidata: Q62051012
  wikipedia: Behrend's theorem
inventory: [HVKZZE1H8C]
---

## Statement

In arithmetic combinatorics, **Behrend's theorem** states that the subsets of the [[integers|0C4JS9RF5M]] from 1 to $n$ in which no member of the set is a multiple of any other must have a logarithmic density that goes to zero as $n$ becomes large. The theorem is named after Felix Behrend, who published it in 1935.