"Frobenius number" meaning in All languages combined

{
  "etymology_text": "After Ferdinand Georg Frobenius.",
  "forms": [
    {
      "form": "Frobenius numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Frobenius number (plural Frobenius numbers)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "The Frobenius number of 2 and 5 is 3, since 3 cannot be formed as a sum of twos and fives while every larger integer can.",
          "type": "example"
        }
      ],
      "glosses": [
        "For a given set of coprime positive integers, the greatest integer that cannot be expressed as a linear combination (with nonnegative integer coefficients) of its elements."
      ],
      "id": "en-Frobenius_number-en-noun--WWdi7mn",
      "links": [
        [
          "coprime",
          "coprime"
        ],
        [
          "positive",
          "positive"
        ],
        [
          "integer",
          "integer"
        ],
        [
          "linear combination",
          "linear combination"
        ]
      ]
    }
  ],
  "word": "Frobenius number"
}

{
  "etymology_text": "After Ferdinand Georg Frobenius.",
  "forms": [
    {
      "form": "Frobenius numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Frobenius number (plural Frobenius numbers)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with usage examples",
        "Pages with 1 entry",
        "Pages with entries"
      ],
      "examples": [
        {
          "text": "The Frobenius number of 2 and 5 is 3, since 3 cannot be formed as a sum of twos and fives while every larger integer can.",
          "type": "example"
        }
      ],
      "glosses": [
        "For a given set of coprime positive integers, the greatest integer that cannot be expressed as a linear combination (with nonnegative integer coefficients) of its elements."
      ],
      "links": [
        [
          "coprime",
          "coprime"
        ],
        [
          "positive",
          "positive"
        ],
        [
          "integer",
          "integer"
        ],
        [
          "linear combination",
          "linear combination"
        ]
      ]
    }
  ],
  "word": "Frobenius number"
}