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Diophantine equation

Syllabification: Di·o·phan·tine e·qua·tion
Pronunciation: /ˌdīəˈfanˌtin, -tīn

Definition of Diophantine equation in English:


A polynomial equation with integral coefficients for which integral solutions are required.
Example sentences
  • That conjecture offers a new way of expressing Diophantine problems, in effect translating an infinite number of Diophantine equations (including the equation of Fermat's last theorem) into a single mathematical statement.
  • Instead of asking whether a given Diophantine equation has a solution, ask ‘for what equations do known methods yield the answer?’
  • Wolfram displays a table of some of the simplest possible Diophantine equations, distinguishing between those known to have integer solutions, those known to have no integer solutions, and those for which the question is still open.


early 18th century: named after Diophantus.

Definition of Diophantine equation in:

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