Diophantine equation

English

Alternative forms

• diophantine equation

Noun

Diophantine equation (plural Diophantine equations)

1. (number theory) A polynomial equation whose variables are only permitted to assume integer values.
   • 1993, Ross Talent, Alf van der Poorten (translation editors), Vladimir G. Sprindžuk, Classical Diophantine Equations, Springer, Lecture Notes in Mathematics 1559, page viii,

     Nevertheless, 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.

   • 2005, Harold Davenport, edited by T. D. Browning, Analytic Methods for Diophantine Equations and Diophantine Inequalities, 2nd edition, Cambridge University Press, page i:

     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.

   • 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,

     The following theorem determines the criteria for the solvability of [a] neutrosophic linear Diophantine equation.

Hyponyms

• Pell’s equation

Derived terms

• exponential Diophantine equation

Related terms

• Diophantine analysis
• Diophantine set

Translations

polynomial equation of integer variables

• Catalan: equació diofàntica f
• Chinese:

  Cantonese: 丟番圖方程／丢番图方程 (diu¹ faan¹ tou⁴ fong¹ cing⁴)

  Mandarin: 丟番圖方程／丢番图方程 (Diūfāntú fāngchéng)

• Finnish: Diofantoksen yhtälö
• French: équation diophantienne f
• German: diophantische Gleichung f
• Hungarian: diophantoszi egyenlet
• Italian: equazione diofantea, equazione diofantina
• Japanese: ディオファントス方程式
• Portuguese: equação diofantina f
• Romanian: ecuație diofantică f
• Russian: диафа́нтово уравне́ние n (diafántovo uravnénije)
• Spanish: ecuación diofántica f, ecuación diofantina f
• Swedish: diofantisk ekvation (sv) c

Further reading

• Hilbert's tenth problem on Wikipedia.Wikipedia