"Diophantine equation" meaning in English

See Diophantine equation in All languages combined, or Wiktionary

Noun

Forms: Diophantine equations [plural]
Head templates: {{en-noun}} Diophantine equation (plural Diophantine equations)
  1. (number theory) A polynomial equation whose variables are only permitted to assume integer values. Wikipedia link: Diophantine equation, simple:Diophantine equation Categories (topical): Algebra, Mathematics, Number theory Synonyms: diophantine equation Hyponyms: Pell’s equation Derived forms: exponential Diophantine equation Related terms: Diophantine analysis, Diophantine set Translations (polynomial equation of integer variables): equació diofàntica [feminine] (Catalan), 丟番圖方程 (Chinese Cantonese), 丢番图方程 (diu¹ faan¹ tou⁴ fong¹ cing⁴) (Chinese Cantonese), 丟番圖方程 (Chinese Mandarin), 丢番图方程 (Diūfāntú fāngchéng) (Chinese Mandarin), Diofantoksen yhtälö (Finnish), équation diophantienne [feminine] (French), diophantische Gleichung [feminine] (German), diophantoszi egyenlet (Hungarian), equazione diofantea (Italian), equazione diofantina (Italian), ディオファントス方程式 (Japanese), equação diofantina [feminine] (Portuguese), ecuație diofantică [feminine] (Romanian), диафа́нтово уравне́ние (diafántovo uravnénije) [neuter] (Russian), ecuación diofántica [feminine] (Spanish), ecuación diofantina [feminine] (Spanish), diofantisk ekvation [common-gender] (Swedish)

Inflected forms

{
  "forms": [
    {
      "form": "Diophantine equations",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Diophantine equation (plural Diophantine equations)",
      "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": "English entries with topic categories using raw markup",
          "parents": [
            "Entries with topic categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Mandarin terms with redundant transliterations",
          "parents": [
            "Terms with redundant transliterations",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Cantonese translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Catalan translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Finnish translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with French translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with German translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Hungarian translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Italian translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Japanese translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Mandarin translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Portuguese translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Romanian translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Russian translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Spanish translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Swedish translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Number theory",
          "orig": "en:Number theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "derived": [
        {
          "word": "exponential Diophantine equation"
        }
      ],
      "examples": [
        {
          "text": "1993, Ross Talent, Alf van der Poorten (translation editors), Vladimir G. Sprindžuk, Classical Diophantine Equations, Springer, Lecture Notes in Mathematics 1559, page viii,\nNevertheless, the fundamental idea of Skolem's method, the reduction of algebraic diophantine equations to exponential equations, has shown exceptional vitality in recent episodes of the theory of diophantine equations."
        },
        {
          "ref": "2005, Harold Davenport, edited by T. D. Browning, Analytic Methods for Diophantine Equations and Diophantine Inequalities, 2nd edition, Cambridge University Press, page i",
          "text": "Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities.",
          "type": "quotation"
        },
        {
          "text": "2020, Hasan Sankari, Mohammad Abobala, Neutrosophic Linear Diophantine Equations With Two Variables, in Neutrosophic Sets and Systems, Volume 38, University of New Mexico, page 402,\nThe following theorem determines the criteria for the solvability of [a] neutrosophic linear Diophantine equation."
        }
      ],
      "glosses": [
        "A polynomial equation whose variables are only permitted to assume integer values."
      ],
      "hyponyms": [
        {
          "word": "Pell’s equation"
        }
      ],
      "id": "en-Diophantine_equation-en-noun-bu1J3iG0",
      "links": [
        [
          "number theory",
          "number theory"
        ],
        [
          "polynomial",
          "polynomial"
        ],
        [
          "equation",
          "equation"
        ],
        [
          "variable",
          "variable"
        ],
        [
          "permit",
          "permit"
        ],
        [
          "assume",
          "assume"
        ],
        [
          "integer",
          "integer"
        ],
        [
          "value",
          "value"
        ]
      ],
      "raw_glosses": [
        "(number theory) A polynomial equation whose variables are only permitted to assume integer values."
      ],
      "related": [
        {
          "word": "Diophantine analysis"
        },
        {
          "word": "Diophantine set"
        }
      ],
      "synonyms": [
        {
          "word": "diophantine equation"
        }
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "translations": [
        {
          "code": "ca",
          "lang": "Catalan",
          "sense": "polynomial equation of integer variables",
          "tags": [
            "feminine"
          ],
          "word": "equació diofàntica"
        },
        {
          "code": "yue",
          "lang": "Chinese Cantonese",
          "sense": "polynomial equation of integer variables",
          "word": "丟番圖方程"
        },
        {
          "code": "yue",
          "lang": "Chinese Cantonese",
          "roman": "diu¹ faan¹ tou⁴ fong¹ cing⁴",
          "sense": "polynomial equation of integer variables",
          "word": "丢番图方程"
        },
        {
          "code": "cmn",
          "lang": "Chinese Mandarin",
          "sense": "polynomial equation of integer variables",
          "word": "丟番圖方程"
        },
        {
          "code": "cmn",
          "lang": "Chinese Mandarin",
          "roman": "Diūfāntú fāngchéng",
          "sense": "polynomial equation of integer variables",
          "word": "丢番图方程"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "polynomial equation of integer variables",
          "word": "Diofantoksen yhtälö"
        },
        {
          "code": "fr",
          "lang": "French",
          "sense": "polynomial equation of integer variables",
          "tags": [
            "feminine"
          ],
          "word": "équation diophantienne"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "polynomial equation of integer variables",
          "tags": [
            "feminine"
          ],
          "word": "diophantische Gleichung"
        },
        {
          "code": "hu",
          "lang": "Hungarian",
          "sense": "polynomial equation of integer variables",
          "word": "diophantoszi egyenlet"
        },
        {
          "code": "it",
          "lang": "Italian",
          "sense": "polynomial equation of integer variables",
          "word": "equazione diofantea"
        },
        {
          "code": "it",
          "lang": "Italian",
          "sense": "polynomial equation of integer variables",
          "word": "equazione diofantina"
        },
        {
          "code": "ja",
          "lang": "Japanese",
          "sense": "polynomial equation of integer variables",
          "word": "ディオファントス方程式"
        },
        {
          "code": "pt",
          "lang": "Portuguese",
          "sense": "polynomial equation of integer variables",
          "tags": [
            "feminine"
          ],
          "word": "equação diofantina"
        },
        {
          "code": "ro",
          "lang": "Romanian",
          "sense": "polynomial equation of integer variables",
          "tags": [
            "feminine"
          ],
          "word": "ecuație diofantică"
        },
        {
          "code": "ru",
          "lang": "Russian",
          "roman": "diafántovo uravnénije",
          "sense": "polynomial equation of integer variables",
          "tags": [
            "neuter"
          ],
          "word": "диафа́нтово уравне́ние"
        },
        {
          "code": "es",
          "lang": "Spanish",
          "sense": "polynomial equation of integer variables",
          "tags": [
            "feminine"
          ],
          "word": "ecuación diofántica"
        },
        {
          "code": "es",
          "lang": "Spanish",
          "sense": "polynomial equation of integer variables",
          "tags": [
            "feminine"
          ],
          "word": "ecuación diofantina"
        },
        {
          "code": "sv",
          "lang": "Swedish",
          "sense": "polynomial equation of integer variables",
          "tags": [
            "common-gender"
          ],
          "word": "diofantisk ekvation"
        }
      ],
      "wikipedia": [
        "Diophantine equation",
        "simple:Diophantine equation"
      ]
    }
  ],
  "word": "Diophantine equation"
}
{
  "derived": [
    {
      "word": "exponential Diophantine equation"
    }
  ],
  "forms": [
    {
      "form": "Diophantine equations",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Diophantine equation (plural Diophantine equations)",
      "name": "en-noun"
    }
  ],
  "hyponyms": [
    {
      "word": "Pell’s equation"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "Diophantine analysis"
    },
    {
      "word": "Diophantine set"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English entries with topic categories using raw markup",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with non-redundant non-automated sortkeys",
        "English terms with quotations",
        "Mandarin terms with redundant transliterations",
        "Pages with 1 entry",
        "Terms with Cantonese translations",
        "Terms with Catalan translations",
        "Terms with Finnish translations",
        "Terms with French translations",
        "Terms with German translations",
        "Terms with Hungarian translations",
        "Terms with Italian translations",
        "Terms with Japanese translations",
        "Terms with Mandarin translations",
        "Terms with Portuguese translations",
        "Terms with Romanian translations",
        "Terms with Russian translations",
        "Terms with Spanish translations",
        "Terms with Swedish translations",
        "en:Algebra",
        "en:Mathematics",
        "en:Number theory"
      ],
      "examples": [
        {
          "text": "1993, Ross Talent, Alf van der Poorten (translation editors), Vladimir G. Sprindžuk, Classical Diophantine Equations, Springer, Lecture Notes in Mathematics 1559, page viii,\nNevertheless, the fundamental idea of Skolem's method, the reduction of algebraic diophantine equations to exponential equations, has shown exceptional vitality in recent episodes of the theory of diophantine equations."
        },
        {
          "ref": "2005, Harold Davenport, edited by T. D. Browning, Analytic Methods for Diophantine Equations and Diophantine Inequalities, 2nd edition, Cambridge University Press, page i",
          "text": "Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities.",
          "type": "quotation"
        },
        {
          "text": "2020, Hasan Sankari, Mohammad Abobala, Neutrosophic Linear Diophantine Equations With Two Variables, in Neutrosophic Sets and Systems, Volume 38, University of New Mexico, page 402,\nThe following theorem determines the criteria for the solvability of [a] neutrosophic linear Diophantine equation."
        }
      ],
      "glosses": [
        "A polynomial equation whose variables are only permitted to assume integer values."
      ],
      "links": [
        [
          "number theory",
          "number theory"
        ],
        [
          "polynomial",
          "polynomial"
        ],
        [
          "equation",
          "equation"
        ],
        [
          "variable",
          "variable"
        ],
        [
          "permit",
          "permit"
        ],
        [
          "assume",
          "assume"
        ],
        [
          "integer",
          "integer"
        ],
        [
          "value",
          "value"
        ]
      ],
      "raw_glosses": [
        "(number theory) A polynomial equation whose variables are only permitted to assume integer values."
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "wikipedia": [
        "Diophantine equation",
        "simple:Diophantine equation"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "diophantine equation"
    }
  ],
  "translations": [
    {
      "code": "ca",
      "lang": "Catalan",
      "sense": "polynomial equation of integer variables",
      "tags": [
        "feminine"
      ],
      "word": "equació diofàntica"
    },
    {
      "code": "yue",
      "lang": "Chinese Cantonese",
      "sense": "polynomial equation of integer variables",
      "word": "丟番圖方程"
    },
    {
      "code": "yue",
      "lang": "Chinese Cantonese",
      "roman": "diu¹ faan¹ tou⁴ fong¹ cing⁴",
      "sense": "polynomial equation of integer variables",
      "word": "丢番图方程"
    },
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "sense": "polynomial equation of integer variables",
      "word": "丟番圖方程"
    },
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "roman": "Diūfāntú fāngchéng",
      "sense": "polynomial equation of integer variables",
      "word": "丢番图方程"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "polynomial equation of integer variables",
      "word": "Diofantoksen yhtälö"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "polynomial equation of integer variables",
      "tags": [
        "feminine"
      ],
      "word": "équation diophantienne"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "polynomial equation of integer variables",
      "tags": [
        "feminine"
      ],
      "word": "diophantische Gleichung"
    },
    {
      "code": "hu",
      "lang": "Hungarian",
      "sense": "polynomial equation of integer variables",
      "word": "diophantoszi egyenlet"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "polynomial equation of integer variables",
      "word": "equazione diofantea"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "polynomial equation of integer variables",
      "word": "equazione diofantina"
    },
    {
      "code": "ja",
      "lang": "Japanese",
      "sense": "polynomial equation of integer variables",
      "word": "ディオファントス方程式"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "polynomial equation of integer variables",
      "tags": [
        "feminine"
      ],
      "word": "equação diofantina"
    },
    {
      "code": "ro",
      "lang": "Romanian",
      "sense": "polynomial equation of integer variables",
      "tags": [
        "feminine"
      ],
      "word": "ecuație diofantică"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "diafántovo uravnénije",
      "sense": "polynomial equation of integer variables",
      "tags": [
        "neuter"
      ],
      "word": "диафа́нтово уравне́ние"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "polynomial equation of integer variables",
      "tags": [
        "feminine"
      ],
      "word": "ecuación diofántica"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "polynomial equation of integer variables",
      "tags": [
        "feminine"
      ],
      "word": "ecuación diofantina"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "polynomial equation of integer variables",
      "tags": [
        "common-gender"
      ],
      "word": "diofantisk ekvation"
    }
  ],
  "word": "Diophantine equation"
}

Download raw JSONL data for Diophantine equation meaning in English (5.6kB)


This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-09-01 from the enwiktionary dump dated 2024-08-20 using wiktextract (8e41825 and f99c758). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.