---
tag: WFQDNE306H
kind: statement
role: theorem
name: Newman-Znám theorem
sources:
  - wikipedia: en:3603349@r1357173515
    locator: Herzog–Schönheim conjecture, section Mirsky–Newman theorem > Newman-Znám theorem
    note: adopted
    mention: wikipedia://en/3603349#J5OQ
    sections: [Statement]
inventory: [34TNBNNA28]
---

## Statement

Štefan Znám in 1968 and subsequently Morris Newman in 1971 proved a general form of Mirsky–Newman theorem, namely given a disjoint covering system, suppose the maximum of the moduli $n$ occurs $l$ times, then $l \geq p$, the smallest prime dividing $n$. In 1986, an non-analytic proof of this general result was given.