See Diophantine equation on Wiktionary
{ "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": "Entries with translation boxes", "parents": [], "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": "Pages with entries", "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^([Davenport]) 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": "quote" }, { "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 lemmas", "English multiword terms", "English nouns", "English terms with quotations", "Entries with translation boxes", "Mandarin terms with redundant transliterations", "Pages with 1 entry", "Pages with entries", "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^([Davenport]) 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": "quote" }, { "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" }
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