{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Statement\n\nŠtefan 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.\n",
  "commit": "a799a9852bcfeae9dc83faa3bef60208bb53686b",
  "front": {
    "inventory": [
      "34TNBNNA28"
    ],
    "kind": "statement",
    "name": "Newman-Znám theorem",
    "role": "theorem",
    "sources": [
      {
        "locator": "Herzog–Schönheim conjecture, section Mirsky–Newman theorem \u003e Newman-Znám theorem",
        "mention": "wikipedia://en/3603349#J5OQ",
        "note": "adopted",
        "sections": [
          "Statement"
        ],
        "wikipedia": "en:3603349@r1357173515"
      }
    ],
    "tag": "WFQDNE306H"
  },
  "kind": "statement",
  "link": "https://math2.tamnd.com/node/WFQDNE306H/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/WFQDNE306H.md",
  "msc": null,
  "name": "Newman-Znám theorem",
  "prov": null,
  "role": "theorem",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/WFQ/WFQDNE306H.md",
  "status": null,
  "tag": "WFQDNE306H",
  "uri": "m2://WFQDNE306H",
  "url": "https://math2.tamnd.com/wiki/newman-znam-theorem/",
  "writing": {
    "tag": "WFQDNE306H",
    "kind": "statement",
    "level": "W0",
    "next": [
      {
        "what": "edge uses out",
        "note": "each definition that the statement needs",
        "have": 0,
        "want": 1
      }
    ]
  }
}