"abc conjecture" meaning in All languages combined

{
  "etymology_text": "From the names of the variables a, b, and c. The conjecture was proposed in 1985.",
  "forms": [
    {
      "form": "abc conjectures",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "head": "abc conjecture"
      },
      "expansion": "abc conjecture (plural abc conjectures)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Number theory",
          "orig": "en:Number theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "68 32",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "64 36",
          "kind": "other",
          "name": "English terms containing italics",
          "parents": [
            "Terms containing italics",
            "Terms by orthographic property",
            "Terms by lexical property"
          ],
          "source": "w+disamb"
        }
      ],
      "examples": [
        {
          "text": "1985, Paul Vojta, Appendix, Serge Lang, Introduction to Arakelov Theory, Springer, 1988 Softcover, page 156,\nFinally in §5 we give one application to the curve X⁴ + Y⁴ = Z⁴, showing that the height inequalities for the curve imply the asymptotic Fermat conjecture and a weak form of the Masser-Oesterlé abc''' conjecture."
        },
        {
          "ref": "2004, Sergei K. Lando, R.V. Gamkrelidze, V.A. Vassiliev, Graphs on Surfaces and Their Applications, Springer, page 137",
          "text": "The abc conjecture may well replace the Fermat theorem for the future generation of mathematicians.",
          "type": "quotation"
        },
        {
          "ref": "2006, Pei-Chu Hu, Chung-Chun Yang, Value Distribution Theory Related to Number Theory, Springer (Birkhäuser), page 233",
          "text": "To prove or disprove the abc-conjecture would be an important contribution to number theory.[…]Langevin ([236], [237]) proved that the abc-conjecture implies the Erdős-Woods conjecture with k = 3 except perhaps a finite number of counter examples.",
          "type": "quotation"
        },
        {
          "ref": "2007, Enrico Bombieri, Walter Gubler, Heights in Diophantine Geometry, Cambridge University Press, page 401",
          "text": "The abc-conjecture of Masser and Oesterle is a typical example of a simple statement that can be used to unify and motivate many results in number theory, which otherwise would be scattered statements without a common link.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Given coprime positive integers a, b and c, such that a + b = c, and d the radical of abc (the product of its distinct prime factors), the conjecture that d is usually not much smaller than c (in other words, that if a and b are divisible by large powers of primes, then c usually is not)."
      ],
      "id": "en-abc_conjecture-en-noun-tjhQLeNJ",
      "links": [
        [
          "number theory",
          "number theory"
        ],
        [
          "coprime",
          "coprime"
        ],
        [
          "positive",
          "positive"
        ],
        [
          "integer",
          "integer"
        ],
        [
          "radical",
          "radical"
        ],
        [
          "product",
          "product"
        ],
        [
          "prime",
          "prime"
        ],
        [
          "conjecture",
          "conjecture"
        ]
      ],
      "raw_glosses": [
        "(number theory) Given coprime positive integers a, b and c, such that a + b = c, and d the radical of abc (the product of its distinct prime factors), the conjecture that d is usually not much smaller than c (in other words, that if a and b are divisible by large powers of primes, then c usually is not)."
      ],
      "synonyms": [
        {
          "_dis1": "70 30",
          "sense": "conjecture in number theory",
          "word": "Oesterlé-Masser conjecture"
        }
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "translations": [
        {
          "_dis1": "70 30",
          "code": "fr",
          "lang": "French",
          "sense": "conjecture in number theory",
          "tags": [
            "feminine"
          ],
          "word": "conjecture abc"
        },
        {
          "_dis1": "70 30",
          "code": "de",
          "lang": "German",
          "sense": "conjecture in number theory",
          "tags": [
            "feminine"
          ],
          "word": "abc-Vermutung"
        },
        {
          "_dis1": "70 30",
          "code": "it",
          "lang": "Italian",
          "sense": "conjecture in number theory",
          "tags": [
            "feminine"
          ],
          "word": "congettura abc"
        },
        {
          "_dis1": "70 30",
          "code": "pt",
          "lang": "Portuguese",
          "sense": "conjecture in number theory",
          "tags": [
            "feminine"
          ],
          "word": "conjetura abc"
        },
        {
          "_dis1": "70 30",
          "code": "es",
          "lang": "Spanish",
          "sense": "conjecture in number theory",
          "tags": [
            "feminine"
          ],
          "word": "conjetura abc"
        }
      ]
    },
    {
      "glosses": [
        "Any of certain generalisations of the conjecture."
      ],
      "id": "en-abc_conjecture-en-noun-vso3Mh3v"
    }
  ],
  "synonyms": [
    {
      "_dis1": "54 46",
      "word": "abc-conjecture"
    },
    {
      "_dis1": "54 46",
      "word": "ABC conjecture"
    }
  ],
  "wikipedia": [
    "abc conjecture"
  ],
  "word": "abc conjecture"
}

{
  "categories": [
    "English countable nouns",
    "English entries with incorrect language header",
    "English lemmas",
    "English multiword terms",
    "English nouns",
    "English terms containing italics"
  ],
  "etymology_text": "From the names of the variables a, b, and c. The conjecture was proposed in 1985.",
  "forms": [
    {
      "form": "abc conjectures",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "head": "abc conjecture"
      },
      "expansion": "abc conjecture (plural abc conjectures)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English terms with quotations",
        "en:Number theory"
      ],
      "examples": [
        {
          "text": "1985, Paul Vojta, Appendix, Serge Lang, Introduction to Arakelov Theory, Springer, 1988 Softcover, page 156,\nFinally in §5 we give one application to the curve X⁴ + Y⁴ = Z⁴, showing that the height inequalities for the curve imply the asymptotic Fermat conjecture and a weak form of the Masser-Oesterlé abc''' conjecture."
        },
        {
          "ref": "2004, Sergei K. Lando, R.V. Gamkrelidze, V.A. Vassiliev, Graphs on Surfaces and Their Applications, Springer, page 137",
          "text": "The abc conjecture may well replace the Fermat theorem for the future generation of mathematicians.",
          "type": "quotation"
        },
        {
          "ref": "2006, Pei-Chu Hu, Chung-Chun Yang, Value Distribution Theory Related to Number Theory, Springer (Birkhäuser), page 233",
          "text": "To prove or disprove the abc-conjecture would be an important contribution to number theory.[…]Langevin ([236], [237]) proved that the abc-conjecture implies the Erdős-Woods conjecture with k = 3 except perhaps a finite number of counter examples.",
          "type": "quotation"
        },
        {
          "ref": "2007, Enrico Bombieri, Walter Gubler, Heights in Diophantine Geometry, Cambridge University Press, page 401",
          "text": "The abc-conjecture of Masser and Oesterle is a typical example of a simple statement that can be used to unify and motivate many results in number theory, which otherwise would be scattered statements without a common link.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Given coprime positive integers a, b and c, such that a + b = c, and d the radical of abc (the product of its distinct prime factors), the conjecture that d is usually not much smaller than c (in other words, that if a and b are divisible by large powers of primes, then c usually is not)."
      ],
      "links": [
        [
          "number theory",
          "number theory"
        ],
        [
          "coprime",
          "coprime"
        ],
        [
          "positive",
          "positive"
        ],
        [
          "integer",
          "integer"
        ],
        [
          "radical",
          "radical"
        ],
        [
          "product",
          "product"
        ],
        [
          "prime",
          "prime"
        ],
        [
          "conjecture",
          "conjecture"
        ]
      ],
      "raw_glosses": [
        "(number theory) Given coprime positive integers a, b and c, such that a + b = c, and d the radical of abc (the product of its distinct prime factors), the conjecture that d is usually not much smaller than c (in other words, that if a and b are divisible by large powers of primes, then c usually is not)."
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ]
    },
    {
      "glosses": [
        "Any of certain generalisations of the conjecture."
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "conjecture in number theory",
      "word": "Oesterlé-Masser conjecture"
    },
    {
      "word": "abc-conjecture"
    },
    {
      "word": "ABC conjecture"
    }
  ],
  "translations": [
    {
      "code": "fr",
      "lang": "French",
      "sense": "conjecture in number theory",
      "tags": [
        "feminine"
      ],
      "word": "conjecture abc"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "conjecture in number theory",
      "tags": [
        "feminine"
      ],
      "word": "abc-Vermutung"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "conjecture in number theory",
      "tags": [
        "feminine"
      ],
      "word": "congettura abc"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "conjecture in number theory",
      "tags": [
        "feminine"
      ],
      "word": "conjetura abc"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "conjecture in number theory",
      "tags": [
        "feminine"
      ],
      "word": "conjetura abc"
    }
  ],
  "wikipedia": [
    "abc conjecture"
  ],
  "word": "abc conjecture"
}